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School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 3. Solutions. Problem 1. Here we systematically develop the solution of the system (11.2.4), which is the formula for hi , that satises the recursion hi = phi+1 + qhi1 , h0 = 1. (1) a. Show that any constant solution hi = A satises (1).
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
Clear@y, x, starterx, starteryD; starterx = 1.71; startery = 18.06; sol = DSolve@8y '@xD = 3 y@xD, y@starterxD = startery<, y@xD, xD; y@xD . sol@1DD Growth Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 Publisher: Math Everywhere, Inc. Version
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
f@xD = a x + b, The calculation reveals that when you take a line function f@x + hD - f@xD = a h. then you find that This tells you that when x advances by h units, then f@xD grows by Consequently a line function f@xD = a x + b has constant growth rate of
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 5 Due Tuesday November 19, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon5s ol.pdf. Google automatic ally generates html vers ions of doc uments as we c rawl
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Examples for 09/26/2011 Fall 2011 Normal (Gaussian) Distribution. mean standard deviation N ,2 f (x ) = 1 2 e -( x - ) 2 2 2 , - < x < . Standard Normal Distribution N ( 0 , 1 ): Z ~ N( 0, 1 ) X ~ N ( , 2 ) Z = X - = 0, 2 = 1. X = +Z _ EXCEL
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Class notes, MATH 564 Lee DeVille November 18, 2013 2 Contents I Background 7 1 Introduction 9 2 Set and Measure Theory 2.1 Notation about limits and sets . . . . . . . . . . 2.1.1 Sequences and Limits . . . . . . . . . . . 2.1.2 Sets and Limits . . . . .
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Least squares Denition 1. x is a least squares solution of the system Ax = b if x is such that Ax b is as small as possible. If Ax = b is consistent, then Interesting case: Ax = b is inconsistent. (in other words: the system is overdetermined) Idea. Ax
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Orthogonal bases Recall: Suppose that v1, vn are independent. , vn are nonzero and (pairwise) orthogonal. Then v1, , Denition 1. A basis v1, , vn of a vector space V is an orthogonal basis if the vectors are (pairwise) orthogonal. 0 1 1 vectors 1 , 1 , 0
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
GramSchmidt Recipe: (GramSchmidt orthonormalization) Given a basis a1, , an, produce an orthonormal basis q1, b1 = a1, b2 = a2 a2, q1 q1, Example 2. Find an orthonormal basis for V = span , qn . b1 b1 b q2 = 2 b2 q1 = 2 1 0 1 , 0 0 0 0 1 1 , 1 . 1
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Application: directed graphs 1 2 1 Graphs appear in network analysis (e.g. internet) or circuit analysis. arrow indicates direction of ow no edges from a node to itself 2 3 3 4 5 at most one edge between nodes 4 Denition 1. Let G be a graph with m edg
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Orthogonality The inner product and distances Denition 1. The inner product (or dot product) of v, w in Rn: v w = v T w = v 1w 1 + + vnwn. Example 2. For instance, 1 1 2 1 = 3 2 Denition 3. The norm (or length) of a vector v in Rn is = v vv = 2 v1 + 2
School: University Of Illinois, Urbana Champaign
Course: Calculus II
Group: Name: Math 231 A. Fall 2014. Worksheet 2. 8/28/14 1. Evaluate using integration by parts (a) arctan x dx (b) ln x dx x2 (c) t3 et dt. 2 (Hint: Substitute x = t2 ) 2. (a) Integrate by parts to get a formula for (b) Evaluate x dx e (b) (ln x)2 dx. co
School: University Of Illinois, Urbana Champaign
Course: MATH
SURVEYUNTUKPENGEMBANGANUIBSECARABERKELANJUTAN KEPADAMAHASISWABARUANGKATAN2014/2015 PETUNJUKPENGISIANANGKET: Pengisiangket dirahasiakan identitasnya.JikakelakidentitasAndaakandigunakan,makakamiakanmintapersetujuanAndaterlebih dahulu. KEBEBASAN dan KEJUJURA
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
EXAM 1 REVIEW MATH 124 (1) All of the students in a class of 30 are majoring in either engineering, math, or both. If 22 are majoring in engineering and 16 are majoring in math, how many students are majoring in engineering but not in math? [Hint: Use a V
School: University Of Illinois, Urbana Champaign
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School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on February 24th and 26th 1. Find an explicit description of Nul(A), where A= 1 3 5 0 0 1 4 2 . x1 x Solution. We rst bring the augmented matrix of the equation A 2 = 0 into reduced x3 x4 echelon form:
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review/Outlook Orthogonal Bases Orthogonal Projection MATH 415 Lecture 23 Monday 16 March 2015 Projection Matrix Review/Outlook Orthogonal Bases Textbook reading: Chapter 3.2. Orthogonal Projection Projection Matrix Review/Outlook Orthogonal Bases Orthogo
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on March 10th and 12th 1 .Find the length of v. Find avector u in the direction of v that has length 1 . 1 Find a vector w that isorthogonal to v. Solution. The length of v is 12 + 12 = 2. Since u = av, we
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review Orthogonal projection on subspaces MATH 415 Lecture 24 Wednesday 18 March 2015 Practice problems Review Orthogonal projection on subspaces Textbook reading: Chapter 3.2, 3.3, 3.4 Practice problems Review Orthogonal projection on subspaces Practice
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on March 3rd and 5th 1. Determine a basis for each of following subspaces: the 4s (i) H = 3s : s, t R , t a b (ii) K = : a 3b + c = 0 , c d 1 2 3 0 0 0 0 1 0 1 , (iii) Col 0 0 0 1 0 1 2 3 0 0 (iv) N
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review Unit Vectors and Orthonormal basis Orthogonality and the Fundamental subspaces Fundamental Theorem of Linear Algeb MATH 415 Lecture 20 Monday, 9 March 2015 Review Unit Vectors and Orthonormal basis Orthogonality and the Fundamental subspaces Fundam
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/19/13 18 K8; This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/EXAMS/EX3/ex 3s olVerB.pdf. Google automatic ally generates html vers ions of doc uments as we c rawl the web. P ag e 1 Math 241 Midte rm 3 (De ce mbe r 5,
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics II
STAT 409 Fall 2012 Name Version A ANSWERS . Exam 1 Page Earned Be sure to show all your work; your partial credit might depend on it. 1 Put your final answers at the end of your work, and mark them clearly. 2 3 No credit will be given without supporting w
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Name _ Version A Exam 2 Page Be sure to show all your work; your partial credit might depend on it. Earned 1 Put your final answers at the end of your work, and mark them clearly. 2 If the answer is a function, its support must be inc
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
Math 416 - Abstract Linear Algebra Fall 2011, section E1 Practice midterm 2 Name: This is a (long) practice exam. The real exam will consist of 4 problems. In the real exam, no calculators, electronic devices, books, or notes may be used. Show your wor
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
Study Aid for Exam # 1, Math 210, Fall 2013 UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Prof. Rick Gorvett Fall, 2008 Exam # 1 (17 Problems Max possible points = 40) Thursday,
School: University Of Illinois, Urbana Champaign
Course: MLC
MATH 471: Actuarial Theory I Midterm #1 October 6, 2010 General Information: 1) There are 9 problems for a total of 50 points. 2) You have between 7:00-8:50pm to write the midterm. 3) You may refer to both sides of one 3in X 5in notecard. 4) You may use a
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 3. Solutions. Problem 1. Here we systematically develop the solution of the system (11.2.4), which is the formula for hi , that satises the recursion hi = phi+1 + qhi1 , h0 = 1. (1) a. Show that any constant solution hi = A satises (1).
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 5 Due Tuesday November 19, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon5s ol.pdf. Google automatic ally generates html vers ions of doc uments as we c rawl
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Fall 2011 Homework #5 (due Friday, October 7, by 3:00 p.m.) 1. Every month, the government of Neverland spends X million dollars purchasing guns and Y million dollars purchasing butter. Assume X and Y jointly follow a Bivariate Normal distributio
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 U3, G4 Fall 2011 Homework #1 (due Friday, September2, by 3:00 p.m.) 1. Below is a list of moment-generating functions. Provide (i) the values for mean and variance 2 , and (ii) P ( 1 X 2 ) for the random variable associated with each moment-gener
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics II
STAT 409 Fall 2011 Homework #11 (due Friday, December 2, by 4:00 p.m.) From the textbook: 8.7-1 ( ) 8.4-2 ( 8th edition ( 8.7-3 ( ) ) 8.4-4 ( ) 8.7-4 ( ) ) 8.7-6 ( 8.4-10 ( ) ) _ 8. In Neverland, annual income (in $) is distributed according to Gamma dist
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 1. Solutions. Problem 1. Prove Proposition 0.2.2. A guide to this problem: start with the open set S = (a, b), for example. First assume that a > , and show that the number a has the properties that it is a lower bound for S , and, for a
School: University Of Illinois, Urbana Champaign
Course: Calculus
MATH 220 Midterm 3 Review This is a sheet of things I think are important to know. Material on the test is not limited to items on this sheet. The test will cover sections 3.10, 4.2, 4.8-4.9, 5.1 - 5.5, 6.1-6.3, 6.5, 7.2. 1. Find the following antiderivat
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 1 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (2 points) Given two nonzero vectors u and v which are not parallel, are u v and v u? 2. (2 points) D
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 3 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Find any three dierent parametrizations of the graph y = x2 . 2. (3 points) Find the equat
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 2 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Find the area of the triangle with vertices P (1, 0, 2), Q(0, 0, 3) and R(7, 4, 3). 2. (3
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 286 E1 The University of Illinois at Urbana-Champaign Department of Mathematics Title of Course: Intro to Differential Equations Plus Room and time: MTWR 1:00-1:50pm in 103 Transportation Building. Instructor: Bogdan Udrea Office location: 241 Illini
School: University Of Illinois, Urbana Champaign
Course: College Algebra
MATH 115 PREPARATION FOR CALCULUS FALL 2013 Instructor Office E-mail Lecture A1 8am 100 Gregory Hall Lecture D1 11am 114 DKH Jennifer McNeilly 121 Altgeld Hall jrmcneil@illinois.edu Lecture X1 Noon 217 Noyes Lab Theodore Molla 226 Illini Hall molla@illino
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Syllabus for the Midterm Exam on February 23 * Systems of linear equations and their applications (Sections 1.1, 1.2) * Gaussian elimination, row-echelon form (Section 1.2) * Matrix operations (Sections 1.3, 1.4, 1.5) * Nonsingular matrices, computing
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
MATH416AbstractLinearAlgebra I. GeneralInformation Instructor:BenjaminWyser ContactInfo: TimeandPlace:MWF9:00am 9:50am,141AltgeldHall Email:bwyser@illinois.edu OfficePhone:(217)3000363 OfficeLocation:222AIlliniHall OfficeHours:MWF1:002:00,orby appointment
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/567: ACTUARIAL THEORY II/ TOPICS IN ACTUARIAL THEORY I SPRING 2012 -INSTRUCTOR: Name: Office: Office phone number: E-mail address: Paul H. Johnson, Jr. 361 Altgeld Hall (217)-244-5517 pjohnson@illinois.edu Website: http:/www.math.uiuc.edu/~pjohns
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 286 Sections D1 & X1 Introduction to Differential Equations Plus Spring 2014 Course Information Sheet INSTRUCTOR: Michael Brannan CONTACT INFORMATION: Ofce: 376 Altgeld Hall. Email: mbrannan@illinois.edu COURSE WEB PAGE: http:/www.math.uiuc.edu/~mbra
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 3. Solutions. Problem 1. Here we systematically develop the solution of the system (11.2.4), which is the formula for hi , that satises the recursion hi = phi+1 + qhi1 , h0 = 1. (1) a. Show that any constant solution hi = A satises (1).
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
Clear@y, x, starterx, starteryD; starterx = 1.71; startery = 18.06; sol = DSolve@8y '@xD = 3 y@xD, y@starterxD = startery<, y@xD, xD; y@xD . sol@1DD Growth Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 Publisher: Math Everywhere, Inc. Version
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
f@xD = a x + b, The calculation reveals that when you take a line function f@x + hD - f@xD = a h. then you find that This tells you that when x advances by h units, then f@xD grows by Consequently a line function f@xD = a x + b has constant growth rate of
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 5 Due Tuesday November 19, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon5s ol.pdf. Google automatic ally generates html vers ions of doc uments as we c rawl
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Examples for 09/26/2011 Fall 2011 Normal (Gaussian) Distribution. mean standard deviation N ,2 f (x ) = 1 2 e -( x - ) 2 2 2 , - < x < . Standard Normal Distribution N ( 0 , 1 ): Z ~ N( 0, 1 ) X ~ N ( , 2 ) Z = X - = 0, 2 = 1. X = +Z _ EXCEL
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Fall 2011 Homework #5 (due Friday, October 7, by 3:00 p.m.) 1. Every month, the government of Neverland spends X million dollars purchasing guns and Y million dollars purchasing butter. Assume X and Y jointly follow a Bivariate Normal distributio
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 U3, G4 Fall 2011 Homework #1 (due Friday, September2, by 3:00 p.m.) 1. Below is a list of moment-generating functions. Provide (i) the values for mean and variance 2 , and (ii) P ( 1 X 2 ) for the random variable associated with each moment-gener
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics II
STAT 409 Fall 2011 Homework #11 (due Friday, December 2, by 4:00 p.m.) From the textbook: 8.7-1 ( ) 8.4-2 ( 8th edition ( 8.7-3 ( ) ) 8.4-4 ( ) 8.7-4 ( ) ) 8.7-6 ( 8.4-10 ( ) ) _ 8. In Neverland, annual income (in $) is distributed according to Gamma dist
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Part II Discrete-time Markov chains 61 Chapter 6 Introduction to Stochastic Processes This chapter of the book is modeled on Chapter 1 of [Nor07], but with some additional material and a dierent structure. Denition 6.0.6. Let (, B ) be a probability space
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/19/13 18 K8; This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/EXAMS/EX3/ex 3s olVerB.pdf. Google automatic ally generates html vers ions of doc uments as we c rawl the web. P ag e 1 Math 241 Midte rm 3 (De ce mbe r 5,
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics II
STAT 409 Fall 2012 Name Version A ANSWERS . Exam 1 Page Earned Be sure to show all your work; your partial credit might depend on it. 1 Put your final answers at the end of your work, and mark them clearly. 2 3 No credit will be given without supporting w
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 1. Solutions. Problem 1. Prove Proposition 0.2.2. A guide to this problem: start with the open set S = (a, b), for example. First assume that a > , and show that the number a has the properties that it is a lower bound for S , and, for a
School: University Of Illinois, Urbana Champaign
STAT 409 Fall 2012 Homework #2 ( due Friday, September 14, by 4:00 p.m. ) 1. Let X 1 , X 2 , , X n be a random sample from the distribution with probability density function ( ) f X ( x ) = f X ( x ; ) = 2 + x 1 (1 x ) , a) 0 < x < 1, > 0. ~ Obtain the m
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
y y = f@xD Accumulation Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 a 2.01 Integrals for Measuring Area BASICS B.1) a f @xD x measures the signed area between x b the plot of f @xD and the x-axis
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 1 Due Tuesday September 10, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon1s ol.pdf. Google automatic ally generates html vers ions of doc uments as we c raw
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics II
MATH/STAT 409 Homework # 3 due 09/20/2013 1. Let > 0 and let X1 , X2 , . . . , Xn be a random sample of size n from a distribution with pdf f (x; ) = 43 x , 0 < x < . 4 (a) Find the MLE . (b) Is a consistent estimator? Justify your answer. (c) Is an unbia
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Class notes, MATH 564 Lee DeVille November 18, 2013 2 Contents I Background 7 1 Introduction 9 2 Set and Measure Theory 2.1 Notation about limits and sets . . . . . . . . . . 2.1.1 Sequences and Limits . . . . . . . . . . . 2.1.2 Sets and Limits . . . . .
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #10 (due Friday, April 6, by 3:00 p.m.) 1. Let X and Y have the joint p.d.f. f X Y ( x , y ) = 20 x 2 y 3 , 0 < x < 1, 0 < y < x, zero elsewhere. a) Find f X | Y ( x | y ). b) Find E ( X | Y = y ). c) Find f Y | X ( y | x ).
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Intro To Abstract Algebra
1 Homework I: June 19, 2009 1.9. Find a formula for 1 + is correct. n j =1 j !j ; use induction to prove that your formula A list of the sums for n = 1, 2, 3, 4, 5 is 2, 6, 24, 120, 720. These are factorials; n better, they are 2!, 3!, 4!, 5!, 6!. If we w
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Name _ Version A Exam 2 Page Be sure to show all your work; your partial credit might depend on it. Earned 1 Put your final answers at the end of your work, and mark them clearly. 2 If the answer is a function, its support must be inc
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 2 Due Tuesday September 24, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon2.pdf. Google automatic ally generates html vers ions of doc uments as we c rawl th
School: University Of Illinois, Urbana Champaign
Course: Intro To Abstract Algebra
1 Math 417 Exam I: July 2, 2009; Solutions 1. If a and b are relatively prime and each of them divides an integer n, prove that their product ab also divides n. Here are two proofs (of course, either one suces for full credit). By hypothesis, n = ak = b .
School: University Of Illinois, Urbana Champaign
Course: Engineering Applications Of Calculus
Math 231E. Fall 2013. HW 3 Solutions. Problem 1. Compute the following limits. Justify your answer. a. lim x2 6x + 4 x2 2x + 1 c. lim x1 (x 2)2 x2 6x + 4 b. lim x1 x2 d. lim x1 sin(x6 ) x e. lim x0 ex 1 x2 2x + 1 x1 (x 1)2 f. lim x0 sin(x) x ex 1 Solution
School: University Of Illinois, Urbana Champaign
Course: Intro Differential Equations
HW 71 1. Sec. 3.6: 3. We have x00 + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375; x0 (0) = 0: The characteristic equation is r2 + 100 = 0 =) r = mentary solution is 10i: The compli- xc (t) = c1 cos 10t + c2 sin 10t: r = 5i is not a root of the characteristi
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 2. Solutions. Problem 1. Let X, Y, Z, W be independent U (0, 1) random variables. Use a Monte Carlo method to compute E[XY 2 + eZ cos(W )]. How much computation should you do to be condent in your answer to three decimal places? (Turn in
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
Approximation Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 3.01 Splines BASICS f@x_D = 1 + Sin@xD; g@x_D = 60 + 60 x + 3 x2 - 7 x3 60 + 3 x2 ; Plot@8f@xD, g@xD<, 8x, - 3, 3<, AxesLabel 8"x", "<, P
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Prof. Rick Gorvett Fall, 2011 Homework Assignment # 8 (max. points = 10) Due at the beginning of class on Thursday, November 17, 201
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
Practice Problems 3 1. During a radio trivia contest, the radio station receives phone calls according to Poisson process with the average rate of five calls per minute. Find the probability that the ninth phone call would arrive during the third minute.
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 409 Spring 2012 Homework #11 (due Thursday, April 12, by 4:30 p.m.) 1. 5.1-5 ( ) The p.d.f. of X is f X ( x ) = x 1 , 0 < x < 1, 0 < < . Let Y = 2 ln X. How is Y distributed? a) Determine the probability distribution of Y by finding the c.d.f. of Y F
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #6 1. 3.3-2 (a), 3.3-4 (a) ( , ) 2. 3.3-2 (b), 3.3-4 (b) ( , ) 3. 3.3-2 (c), 3.3-4 (c) ( , ) ( 4. 3.3-8 5. 3.3-24 (a),(b) ) ( ) 6. 3.4-4 ( ) 7. 3.4-8 ( ) 8. Suppose a random variable X has the following probability density fu
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
Growth f@xD 0.34 Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 0.32 Publisher: Math Everywhere, Inc. Version 6.0 1.05 Using the Tools BASICS 0.30 0.28 B.1) Using the derivative for finding maximum values and minimum values You can tell what h
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #4 (due Friday, February 17, by 3:00 p.m.) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Sally sells seashells by the seashore. The daily sales X of
School: University Of Illinois, Urbana Champaign
Course: Alex
STAT 420 (10 points) (due Friday, November 7, by 3:00 p.m.) Homework #10 Fall 2008 1. Can a corporation's annual profit be predicted from information about the company's chief executive officer (CEO)? Forbes (May, 1999) presented data on company profit (
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
Math 416 - Abstract Linear Algebra Fall 2011, section E1 Practice midterm 2 Name: This is a (long) practice exam. The real exam will consist of 4 problems. In the real exam, no calculators, electronic devices, books, or notes may be used. Show your wor
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #4 (due Friday, February 17, by 3:00 p.m.) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Sally sells seashells by the seashore. The daily sales X of
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
Practice Problems 8 1. Suppose that the actual weight of "10-pound" sacks of potatoes varies from sack to sack and that the actual weight may be considered a random variable having a normal distribution with the mean of 10.2 pounds and the standard deviat
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
Study Aid for Exam # 1, Math 210, Fall 2013 UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Prof. Rick Gorvett Fall, 2008 Exam # 1 (17 Problems Max possible points = 40) Thursday,
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
Approximation 5 Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 4 Publisher: Math Everywhere, Inc. Version 6.0 3 3.06 Power Series BASICS 2 1 B.1) Functions defined by power series - 1.5 B.1.a) What is a power series? Why are power series big
School: University Of Illinois, Urbana Champaign
Course: MLC
MATH 471: Actuarial Theory I Midterm #1 October 6, 2010 General Information: 1) There are 9 problems for a total of 50 points. 2) You have between 7:00-8:50pm to write the midterm. 3) You may refer to both sides of one 3in X 5in notecard. 4) You may use a
School: University Of Illinois, Urbana Champaign
Course: Engineering Applications Of Calculus
Math 231E. Fall 2013. HW 2 Solutions. Problem 1. Recall the Taylor series for ex at a = 0. a. Find the Taylor polynomial of degree 4 for f (x) = ex about the point a = 0. Solution: T4 (x) = 1 + x + x2 x3 x4 + +. 2 6 24 b. Use your answer to part (a) to es
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 409 Spring 2012 Homework #12 (due Friday, April 20, by 3:00 p.m.) 1 5. Let the joint probability density function for ( X , Y ) be f ( x, y ) = 1. x+ y 3 0 < x < 2, 0 < y < 1, , zero otherwise. a) Find the probability P ( X > Y ). b) Find the margina
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #5 (due Friday, February 24, by 3:00 p.m.) 1. Suppose a discrete random variable X has the following probability distribution: P( X = k ) = ( ln 2 ) k k! , k = 1, 2, 3, . Recall ( Homework #1 Problem 9 ): This is a valid prob
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #2 (10 points) (due Friday, February 3, by 3:00 p.m.) 1. A bank classifies borrowers as "high risk" or "low risk," and 16% of its loans are made to those in the "high risk" category. Of all the bank's loans, 5% are in default
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
measures out to f @xD * jump. So the accumulated area of all the boxes measures out to Sum@f @xD jump, 8x, a, b - jump, jump<D As n , jump 0, these sums close in on Integrate@f @xD, 8x, a, b<D = a f @xD x. See what happens as n gets large and the jump get
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
L.6) Here are two points 81, 2< and 85, 4< conveniently plotted on the axes below: y 5 Growth Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 85,4< 4 1.01 Growth LITERACY L.1) A function f@xD starts
School: University Of Illinois, Urbana Champaign
Course: Alex
STAT 420 Homework #4 (10 points) (due Friday, September 26, by 3:00 p.m.) Fall 2008 1. Hogg and Ledolter report on an engineer in a textile mill who studies the effects of temperature and time in a process involving dye on the brightness of a synthetic fa
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Actuarial Risk Theory
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 476 / 567 Actuarial Risk Theory Prof. Rick Gorvett Fall, 2010 Homework Assignment # 4 (max. points = 8) Due at the beginning of class on Thursday, October
School: University Of Illinois, Urbana Champaign
STAT 409 Fall 2012 Homework #3 ( due Friday, September 21, by 4:00 p.m. ) 1. Let > 0 and let X 1 , X 2 , , X n be a random sample from the distribution with the probability density function f X (x) = f X ( x ; ) = a) x 2 e x , x > 0. Find the sufficient s
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2014 Homework #4 (due Friday, February 21, by 3:00 p.m.) No credit will be given without supporting work. 1 3. Alex sells Exciting World of Statistics videos over the phone to earn some extra cash during the economic crisis. Only 10% of al
School: University Of Illinois, Urbana Champaign
Course: Hw01&ans
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Actuarial Modeling Prof. Rick Gorvett Spring 2011 Homework Assignment # 1 (max. points = 10) Due at the beginning of class on Thursday, January 2
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2014 Homework #4 (due Friday, February 21, by 3:00 p.m.) No credit will be given without supporting work. 1 3. Alex sells Exciting World of Statistics videos over the phone to earn some extra cash during the economic crisis. Only 10% of al
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
This output reflects the fact that NDSolve first produces a bunch of points and then strings them together with an interpolating function - just as Euler's method does. The formula for this interpolating function is not available, but you can plot it: Gro
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Class notes, MATH 564 Lee DeVille November 18, 2013 2 Contents I Background 7 1 Introduction 9 2 Set and Measure Theory 2.1 Notation about limits and sets . . . . . . . . . . 2.1.1 Sequences and Limits . . . . . . . . . . . 2.1.2 Sets and Limits . . . . .
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Least squares Denition 1. x is a least squares solution of the system Ax = b if x is such that Ax b is as small as possible. If Ax = b is consistent, then Interesting case: Ax = b is inconsistent. (in other words: the system is overdetermined) Idea. Ax
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Orthogonal bases Recall: Suppose that v1, vn are independent. , vn are nonzero and (pairwise) orthogonal. Then v1, , Denition 1. A basis v1, , vn of a vector space V is an orthogonal basis if the vectors are (pairwise) orthogonal. 0 1 1 vectors 1 , 1 , 0
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
GramSchmidt Recipe: (GramSchmidt orthonormalization) Given a basis a1, , an, produce an orthonormal basis q1, b1 = a1, b2 = a2 a2, q1 q1, Example 2. Find an orthonormal basis for V = span , qn . b1 b1 b q2 = 2 b2 q1 = 2 1 0 1 , 0 0 0 0 1 1 , 1 . 1
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Application: directed graphs 1 2 1 Graphs appear in network analysis (e.g. internet) or circuit analysis. arrow indicates direction of ow no edges from a node to itself 2 3 3 4 5 at most one edge between nodes 4 Denition 1. Let G be a graph with m edg
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Orthogonality The inner product and distances Denition 1. The inner product (or dot product) of v, w in Rn: v w = v T w = v 1w 1 + + vnwn. Example 2. For instance, 1 1 2 1 = 3 2 Denition 3. The norm (or length) of a vector v in Rn is = v vv = 2 v1 + 2
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Linear transformations Throughout, V and W are vector spaces. Denition 1. A map T : V W is a linear transformation if T (cx + dy) = cT (x) + dT (y) for all x, y in V and all c, d in R. Example 2. Let A be an m n matrix. Then the map T (x) = Ax is a linear
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Linear independence Review. spancfw_v1, v2, , vm is the set of all linear combinations c 1v 1 + c 2v 2 + spancfw_v1, v2, + cmvm. , vm is a vector space. Example 1. Is span 1 1 1 1 2 1 , , 3 3 1 equal to R3? Solution. The span is equal to R3 if and o
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Solving Ax = 0 and Ax = b Null spaces Denition 1. The null space of a matrix A is Nul(A) = cfw_x : Ax = 0. In other words, if A is m n, then its null space consists of those vectors x R n which solve the homogeneous equation Ax = 0. Theorem 2. If A is m n
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Bases for column and null spaces Bases for null spaces To nd a basis for Nul(A): nd the parametric form of the solutions to Ax = 0, express solutions x as a linear combination of vectors with the free variables as coecients; these vectors form a basis
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Vector spaces and subspaces We have already encountered vectors in Rn. Now, we discuss the general concept of vectors. In place of the space Rn, we think of general vector spaces. Denition 1. A vector space is a nonempty set V of elements, called vectors,
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
The inverse of a matrix 1 Example 1. The inverse of a real number a is denoted as a1. For instance, 71 = 7 and 7 71 = 71 7 = 1. In the context of n n matrix multiplication, the role of 1 is taken by the n n identity matrix 1 1 . In = 1 Denition 2. An n n
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Application: nite dierences Let us apply linear algebra to the boundary value problem d 2u = f (x), dx2 0 1, x u(0) = u(1) = 0. f (x) is given, and the goal is to nd u(x). Physical interpretation: models steady-state temperature distribution in a bar (u(x
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
The geometry of linear equations Adding and scaling vectors Example 1. We have already encountered matrices such as 1 4 2 3 2 1 2 2 . 3 2 2 0 Each column is what we call a (column) vector. In this example, each column vector has 3 entries and so lies in
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
LU decomposition Elementary matrices Example 1. 1 0 0 1 a b c d 0 1 1 0 a b c d a d g a d g 1 0 0 0 2 0 0 0 1 1 0 0 0 1 0 3 0 1 = = b c e f = h i b c e f = h i Denition 2. An elementary matrix is one that is obtained by performing a single elementary
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Matrix operations Basic notation We will use the following notations for an m n matrix A (m rows, n columns). In terms of the columns of A: | | a1 a2 an ] = | | A = [ a1 a2 In terms of the entries of A: a1,1 a1,2 a2,2 a A = 2,1 am,1 am,2 a1,n a2,n ,
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Introduction to systems of linear equations These slides are based on Section 1 in Linear Algebra and its Applications by David C. Lay. Denition 1. A linear equation in the variables x1, ., xn is an equation that can be written as a 1 x 1 + a 2x 2 + + anx
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
T403 Homework Hints and Solutions II 2.1.1 The symmetries of a non square rhombus is isomorphic to that of a (non-square) rectangle. It has four elements and is abelian. Denoting the 180 rotation by and the reection across one of the diagonals by the elem
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Math 415 Exam 2 Review Sheet by Ruth Luo1 Linear independence, dependence, and bases Let cfw_v1 , v2 , ., vn be a set of vectors of a vector space V . cfw_v1 , v2 , ., vn are linearly independent if c1 v1 + c2 v2 + . + cn vn = 0 has only the trivial so
School: University Of Illinois, Urbana Champaign
Course: Complex Variables
Wm cfw_A i NBVL &_ ._ sm(><+ c3): SiMX oasAy + C CDX SMA W :2 (4+ V N , M 1 :5!an CU>1 \/ :1 ? Cm X SM m 2! (why Hz; a 1% MA RF: % 35h " I (ii 3:0 (JED apu de 3 :1 U>02V>0 Sm )6 61.7) Y ,er@"@ gr Lem WL MM JV mwe 41M cfw_Ln wu (H)V)eC, LQVMDOZ V>o
School: University Of Illinois, Urbana Champaign
Course: Complex Variables
LAURENT SERIES AND SINGULARITIES 1. Introduction So far we have studied analytic functions. Locally, such functions are represented by power series. Globally, the bounded ones are constant, the ones that get large as their inputs get large are polynomials
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Print your name in the format 2 last name rst name: ' (CH/Q )lv Section: Netid (as it appears on Pearson account): Math 225 Midterm Ic V March 3, 2015 In what follows you must show your work! An answer with no justication may give you no credit even when
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Print your name in the format m last name, rst name: 1 Jag] (m. Gur Section: Netid (as it appears on Pearson account): Math 225 Midterm Id (Magi) March 3, 2015 In what follows you must show your work! An answer with no justication may give you no credit e
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Print your name in the format last name, rst name: Section: Netid (as it appears on Pearson account): Math 225 Midterm Ia (\cfw_dmy March 3, 2015 In what follows you must show your work! An answer with no justication may give you no credit even when the a
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Print your name in the fo cfw_Zlat last name, rst name. i [a] E Section: Netid (as it appears on Pearson account): r 1 Math 225 Midterm Ib i lot-ML) March 3, 2015 In what follows you must show your work! An answer with no justication may give you no credi
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Math 225, Sections P1 and S1 Review for Midterm 2 April 7, 2015 1. Determinants. Know: the denition of the determinant of a 1 1 matrix, 2 2 matrix, larger matrices via cofactor expansions, see Section 3.1; how a determinant changes after a row operation
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Math 225 Review problems for midterm 1 0. Study the lecture notes and the textbook (Sections 1.1-1.5, 1.7, 2.1-2.3). Review your homework assignments. 1. Let A1 , A2 be the following matrices 1 1 1 1 1 1 1 1 A1 = 2 1 1 1 , A 2 = 2 1 1 1 , 3 2 2 3 3 2 2 2
School: University Of Illinois, Urbana Champaign
Course: Calculus II Honors
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School: University Of Illinois, Urbana Champaign
Course: Calculus II Honors
1 2 R 1. Evaluate x2 ln xdx. Solution. We use integration by parts. Set dv = x2 dx ) v = We have: Z x3 and u = ln x. 3 Z x3 1 dx 3 x Z 2 x x3 dx = ln x 3 3 x3 ln x x ln xdx = 3 x3 = ln x 3 2 x3 + C: 9 R 2. Evaluate arctan xdx. Solution. We use integration
School: University Of Illinois, Urbana Champaign
Course: Calculus II Honors
1 2 3 4 5 6 7 8 9
School: University Of Illinois, Urbana Champaign
Course: Calculus II Honors
1 2 3 4 5 6 7 8 9
School: University Of Illinois, Urbana Champaign
Course: Calculus II Honors
1 2 3 4 5 6 7 8 9 10 11 12 13
School: University Of Illinois, Urbana Champaign
Course: Calculus II
Group: Name: Math 231 A. Fall 2014. Worksheet 2. 8/28/14 1. Evaluate using integration by parts (a) arctan x dx (b) ln x dx x2 (c) t3 et dt. 2 (Hint: Substitute x = t2 ) 2. (a) Integrate by parts to get a formula for (b) Evaluate x dx e (b) (ln x)2 dx. co
School: University Of Illinois, Urbana Champaign
Course: MATH
SURVEYUNTUKPENGEMBANGANUIBSECARABERKELANJUTAN KEPADAMAHASISWABARUANGKATAN2014/2015 PETUNJUKPENGISIANANGKET: Pengisiangket dirahasiakan identitasnya.JikakelakidentitasAndaakandigunakan,makakamiakanmintapersetujuanAndaterlebih dahulu. KEBEBASAN dan KEJUJURA
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
EXAM 1 REVIEW MATH 124 (1) All of the students in a class of 30 are majoring in either engineering, math, or both. If 22 are majoring in engineering and 16 are majoring in math, how many students are majoring in engineering but not in math? [Hint: Use a V
School: University Of Illinois, Urbana Champaign
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School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on February 24th and 26th 1. Find an explicit description of Nul(A), where A= 1 3 5 0 0 1 4 2 . x1 x Solution. We rst bring the augmented matrix of the equation A 2 = 0 into reduced x3 x4 echelon form:
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review/Outlook Orthogonal Bases Orthogonal Projection MATH 415 Lecture 23 Monday 16 March 2015 Projection Matrix Review/Outlook Orthogonal Bases Textbook reading: Chapter 3.2. Orthogonal Projection Projection Matrix Review/Outlook Orthogonal Bases Orthogo
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on March 10th and 12th 1 .Find the length of v. Find avector u in the direction of v that has length 1 . 1 Find a vector w that isorthogonal to v. Solution. The length of v is 12 + 12 = 2. Since u = av, we
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review Orthogonal projection on subspaces MATH 415 Lecture 24 Wednesday 18 March 2015 Practice problems Review Orthogonal projection on subspaces Textbook reading: Chapter 3.2, 3.3, 3.4 Practice problems Review Orthogonal projection on subspaces Practice
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on March 3rd and 5th 1. Determine a basis for each of following subspaces: the 4s (i) H = 3s : s, t R , t a b (ii) K = : a 3b + c = 0 , c d 1 2 3 0 0 0 0 1 0 1 , (iii) Col 0 0 0 1 0 1 2 3 0 0 (iv) N
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review Unit Vectors and Orthonormal basis Orthogonality and the Fundamental subspaces Fundamental Theorem of Linear Algeb MATH 415 Lecture 20 Monday, 9 March 2015 Review Unit Vectors and Orthonormal basis Orthogonality and the Fundamental subspaces Fundam
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review A new perspective on Ax = b Motivation MATH 415 Lecture 21 Wednesday 11 March 2015 Application: Directed graphs Review A new perspective on Ax = b Textbook reading: Chapter 3.1 Motivation Application: Directed graphs Review A new perspective on Ax
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Application: Directed graphs What can we do with A? Summary/Outlook MATH 415 Lecture 22 Friday 13 March 2015 Practice problems Application: Directed graphs What can we do with A? Textbook reading: Chapter 2.5. Summary/Outlook Practice problems Application
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Lecture 16 Math 225 Note Title 31139008 (Low Mew- m ' (MW at J CLU+CU+H+C tf M L225 Vamvmiym M&U:,7J1zw%o MUM Siam cfw_WJVM~-J 1-5 (u. wwacw M 6m Coma/Jwamg g4, Elvip, 1/. Tm big Vac, avg/672. rim<2 was? Ogjvagpwc; a; v. PM Olm we)?
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Lecture 17 Math 225 Note Title 3124;2008 QM - '15-? g 99% [50mm faucuca) 775a Mquazo fm)0%u.,; AIM W152; 379% \/ :47 wwl 1 12m woeefwM r; Hm veov egmfzw : I Q) @0912 CLDZ,~+_M+i cf, 0
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Lecture 15 Math 225 Note Title 3;1312008 lot/moi WVCLMW 147 CL Cm/guruf. mm mam a; we WE vmoa Wagom amdi cw. m cam WfML u mw 4km 02% W (2193144 6194.665 mgzgyamag @cfw_Z a kid: miu. Wk Wawmmlwcif 5m Q3; 35%1W7ma4 92 64a mm j v yaw how, M064,
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Lecture 8 Math 225 Note Title 2;612008 rm 1 f C - cfw_40 w '60, t2 2: ca cfw_2 Eu, f; U m (fie 43 cfw_w 120 ~ W, U t'gw. - - W mag 4; mum.) swam; @021 I Fm 5m mach) 6% fm 24. M cage/51 M2, Was-Mi) may ; 4ng WXM, WWW/.1 : ; [5593] J 6 2 Lg
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Lecture 9 Math 225 W m i? g. W9$ fax pwmgagmmk
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Lecture 3 Math 225 Note Title 1f21f2008 &w% : 57x01 5% (Janka
School: University Of Illinois, Urbana Champaign
Course: Introductory Matrix Theory
Lecture 5 Math 225 Note Title 1f27f2008 : 4 am Wafw'w (g QIJEzw-zim A4,; [Rm 6th X1279? Kerb 19: xe 4' X; Q; fux'ic 9C9 1% WW WUM Cans. Aw Cot a2, 0%,] m 4(4):, W my: 9;: Ha] axmo'h
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/19/13 18 K8; This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/EXAMS/EX3/ex 3s olVerB.pdf. Google automatic ally generates html vers ions of doc uments as we c rawl the web. P ag e 1 Math 241 Midte rm 3 (De ce mbe r 5,
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics II
STAT 409 Fall 2012 Name Version A ANSWERS . Exam 1 Page Earned Be sure to show all your work; your partial credit might depend on it. 1 Put your final answers at the end of your work, and mark them clearly. 2 3 No credit will be given without supporting w
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Name _ Version A Exam 2 Page Be sure to show all your work; your partial credit might depend on it. Earned 1 Put your final answers at the end of your work, and mark them clearly. 2 If the answer is a function, its support must be inc
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
Math 416 - Abstract Linear Algebra Fall 2011, section E1 Practice midterm 2 Name: This is a (long) practice exam. The real exam will consist of 4 problems. In the real exam, no calculators, electronic devices, books, or notes may be used. Show your wor
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
Study Aid for Exam # 1, Math 210, Fall 2013 UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Prof. Rick Gorvett Fall, 2008 Exam # 1 (17 Problems Max possible points = 40) Thursday,
School: University Of Illinois, Urbana Champaign
Course: MLC
MATH 471: Actuarial Theory I Midterm #1 October 6, 2010 General Information: 1) There are 9 problems for a total of 50 points. 2) You have between 7:00-8:50pm to write the midterm. 3) You may refer to both sides of one 3in X 5in notecard. 4) You may use a
School: University Of Illinois, Urbana Champaign
Course: Calculus I
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Math 415 - Midterm 2 Thursday, October 23, 2014 Circle your section: Philipp Hieronymi 2pm 3pm Armin Straub 9am 11am Name: NetID: UIN: Problem 0. [1 point] Write down the number of your discussion section (for instance, AD2 or ADH) and the rst name of you
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Math 415 - Midterm 2 Thursday, October 23, 2014 Circle your section: Philipp Hieronymi 2pm 3pm Armin Straub 9am 11am Name: NetID: UIN: Problem 0. [1 point] Write down the number of your discussion section (for instance, AD2 or ADH) and the rst name of you
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Math 415 - Midterm 2 Thursday, October 23, 2014 Circle your section: Philipp Hieronymi 2pm 3pm Armin Straub 9am 11am Name: NetID: UIN: Problem 0. [1 point] Write down the number of your discussion section (for instance, AD2 or ADH) and the rst name of you
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Math 415 - Midterm 2 Thursday, October 23, 2014 Circle your section: Philipp Hieronymi 2pm 3pm Armin Straub 9am 11am Name: NetID: UIN: Problem 0. [1 point] Write down the number of your discussion section (for instance, AD2 or ADH) and the rst name of you
School: University Of Illinois, Urbana Champaign
Course: Calculus
Math 220 Quiz 1 7 Name Oi l 0 Date This is a closed book closed notebook quiz. Answer each question correctly and justify your answer. Providing just the answer is not worth any credit. 1. (2 points) Find all real numbers a less than 5 such that f 2: e 11
School: University Of Illinois, Urbana Champaign
Course: Calculus
Math 220 Quiz 3 Name Date _ This is a closed book closed notebook quiz. Answer each question correctly and justify your answer. Providing just the answer is not worth any credit. 1. Calculate the following limits. 2_ 44L! slim"? 1. Ind (5E 3)3 ) xfl :_ ~6
School: University Of Illinois, Urbana Champaign
Course: Calculus
Math 220 Quiz 2 Nalejag Date _._ This is a. closed book closed notebook quiz. Answer each question correctly and justify your answer. Providing just the answer is not worth any credit. 1. Let 2. Express the function given below as a. function in the form
School: University Of Illinois, Urbana Champaign
Course: Calculus
NamyAg/L/jYQr Date _. y Math 220 Quiz 4 / [O This is a closed book closed notebook quiz. Answer each question correctly and justify your answer. Providing just the answer is not worth any credit. 1. Find the derivative using the denition of derivative. _
School: University Of Illinois, Urbana Champaign
Course: Calculus
Math 220 Quiz 5 I Somio w This is a. closed book Closed notebook quiz. Answer each question correctly and justify Name your answer. Providing just the answer is not worth any credit. . dy 1. F d . 111 d1: 3; = 111(si112 CwW/C/ M' / , CM 5/1144; 3 2. S
School: University Of Illinois, Urbana Champaign
Course: Calculus
Name Date 1. US 17 runs North~South A highway patrol officers radar unit is parked right next to a billboard, 200 feet from a long straight stretch of US. 17, and En the west side of the highway. Down the highway, 200 ft north from the point on the highwa
School: University Of Illinois, Urbana Champaign
Course: Calculus
Math 220 uly 19, 2010 Name: Evaluate the following limit .7 V3,); ' . (. 7f co . ,0 00 r 5 6f? i 3 2- : L (X. -:_:;= X (i) (if) 3) Find Hm intwvzxls an \x'lm'h f is imrmsing and decreasing 1) Find the: lured maxinmm and minimum \';1111<smcfw_f_ (I) F
School: University Of Illinois, Urbana Champaign
Course: Calculus
Math .2220 Quiz 10 July 23, 2010 47 (UlM 1. A rectangular storage container with an open top is to have a volume of 10 mg. The length of its base is twice its width. Material for the base costs $10 per square meter. Material for the sides costs $6 per squ
School: University Of Illinois, Urbana Champaign
Course: Calculus
Math 220 Quiz 11 July 27, 2010 Name: 1. If the acceleration function of an object is given by 0,0?) = 10 sint + Boost, and you know further that 3(0) : 0 and v(27r) = 0. Find 5305). Here, scfw_t) is the position function and v(t) is the velocity functio
School: University Of Illinois, Urbana Champaign
Course: Calculus
Math 220 Quiz 8 Name Date 1. Find the equation of the tangent line of the function y = sinful: at a: = 0. m: :0 : MK (X20: M0 :2. + o 2. Consider the following function :02 :53 f(x)=1+2x2-3 a) Find the critical numbers of f 100A): 2 X XL :1 " CXZlX"Z\ 2
School: University Of Illinois, Urbana Champaign
Course: Calculus For Engineers
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 6 October 15, 2013 Name: You have fteen minutes to complete this quiz. No electronic devices are permitted during the quiz. Cheating will be punished with at least a zero on this quiz; there may be more severe consequences. Par
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 7 October 22, 2013 Name: You have fteen minutes to complete this quiz. No electronic devices are permitted during the quiz. Cheating will be punished with at least a zero on this quiz; there may be more severe consequences. Par
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 5 October 8, 2013 Name: You have fteen minutes to complete this quiz. No electronic devices are permitted during the quiz. Cheating will be punished with at least a zero on this quiz; there may be more severe consequences. Part
School: University Of Illinois, Urbana Champaign
Course: Calculus
Index S scalar expansion 3-25 scientific notation 3-10 script M-file 5-17 scripts 5-17 search path 2-12 searching documentation 2-10 semicolon to suppress output 3-30 shutting down MATLAB 2-3 singular matrix 3-19 source control systems, interfacing to MAT
School: University Of Illinois, Urbana Champaign
Course: Calculus
Index Help browser 2-8 help functions 2-10 Help Navigator 2-10 hierarchy of graphics objects 4-27 hold 4-7 I if 5-2 images 4-22 imaginary number 3-10 Import Wizard 2-15 importing data 2-15 index in Help browser 2-10 L Launch Pad 2-8 legend 4-3 legend, add
School: University Of Illinois, Urbana Champaign
Course: Calculus
Index multivariate data, organizing 3-24 N newsgroup for MATLAB users 2-10 Notebook 2-15 numbers 3-10 floating-point 3-11 O object properties 4-28 objects finding handles 4-31 graphics 4-26 online help, viewing 2-8 operator 3-11 colon 3-7 output controlli
School: University Of Illinois, Urbana Champaign
Course: Calculus
Index demonstration programs 5-27 demos 5-27 demos, running from the Launch Pad 2-8 desktop for MATLAB 2-4 desktop tools 2-6 determinant of matrix 3-19 development environment 2-2 diag 3-5 display pane in Help browser 2-10 documentation 2-8 E editing comm
School: University Of Illinois, Urbana Champaign
Course: Calculus
Index Symbols : operator 3-7 B bookmarking documentation 2-10 break 5-6 A algorithms vectorizing 5-22 animation 4-34 annotating plots 4-14 ans 3-4 Application Program Interface (API) 1-3 Array Editor 2-13 array operators 3-22 arrays 3-18, 3-21 cell 5-9 ch
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB Getting More Information The MathWorks Web site (www.mathworks.com) contains numerous M-files that have been written by users and MathWorks staff. These are accessible by selecting Downloads. Also, Technical Notes, which is acces
School: University Of Illinois, Urbana Champaign
Course: Calculus
Demonstration Programs Included with MATLAB MATLAB Miscellaneous Demonstration Programs (Continued) makevase Demonstration of a surface of revolution. quatdemo Quaternion rotation. spinner Colorful lines spinning through space. travel Traveling salesman p
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB MATLAB Gallery Demonstration Programs (Continued) modes Graphical demonstration of 12 modes of the L-shaped membrane. quivdemo Graphical demonstration of the quiver function. spharm2 Graphical demonstration of spherical surface h
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB MATLAB Visualization Demonstration Programs (Continued) penny Several views of the penny data. vibes Vibrating L-shaped membrane movie. xfourier Graphical demonstration of Fourier series expansion. xpklein Klein bottle demo. xpso
School: University Of Illinois, Urbana Champaign
Course: Calculus
Demonstration Programs Included with MATLAB MATLAB ODE Suite Demonstration Programs (Continued) chm7ode Stiff problem CHM7 from Enright and Hull. chm9ode Stiff problem CHM9 from Enright and Hull. d1ode Stiff problem, nonlinear with real eigenvalues. fem1o
School: University Of Illinois, Urbana Champaign
Course: Calculus
Demonstration Programs Included with MATLAB MATLAB Numeric Demonstration Programs (Continued) funfuns Demonstration of functions operating on other functions. lotkademo Example of ordinary differential equation solution. quaddemo Adaptive quadrature. quak
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB . MATLAB Matrix Demonstration Programs airfoil Graphical demonstration of sparse matrix from NASA airfoil. buckydem Connectivity graph of the Buckminster Fuller geodesic dome. delsqdemo Finite difference Laplacian on various doma
School: University Of Illinois, Urbana Champaign
Course: Calculus
Demonstration Programs Included with MATLAB Demonstration Programs Included with MATLAB MATLAB includes many demonstration programs that highlight various features and functions. For a complete list of the demos, at the command prompt type help demos To v
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB integration of ordinary differential equations. MATLABs quadrature routines are quad and quadl. The statement Q = quadl(@humps,0,1) computes the area under the curve in the graph and produces Q = 29.8583 Finally, the graph shows
School: University Of Illinois, Urbana Champaign
Course: Calculus
Scripts and Functions 100 90 80 70 60 50 40 30 20 10 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 The graph shows that the function has a local minimum near x = 0.6. The function fminsearch finds the minimizer, the value of x where the function takes on this
School: University Of Illinois, Urbana Champaign
Course: Calculus
Scripts and Functions x = .01:.01:10; y = log10(x); For more complicated code, vectorization options are not always so obvious. When speed is important, however, you should always look for ways to vectorize your algorithms. Preallocation If you cant vecto
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB When you call plot_fhandle with a handle to the sin function and the argument shown below, the resulting evaluation produces a sine wave plot. plot_fhandle(@sin, -pi:0.01:pi) Function Functions A class of functions, called functi
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB The following statement is not allowed because A is not a string, however MATLAB does not generate an error. eig A ans = 65 MATLAB actually takes the eigenvalues of ASCII numeric equivalent of the letter A (which is the number 65
School: University Of Illinois, Urbana Champaign
Course: Calculus
Scripts and Functions However, when using the unquoted form, MATLAB cannot return output arguments. For example, legend apples oranges creates a legend on a plot using the strings apples and oranges as labels. If you want the legend command to return its
School: University Of Illinois, Urbana Champaign
Course: Calculus
Scripts and Functions Scripts and Functions MATLAB is a powerful programming language as well as an interactive computational environment. Files that contain code in the MATLAB language are called M-files. You create M-files using a text editor, then use
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB Many M-files work this way. If no output argument is supplied, the result is stored in ans. If the second input argument is not supplied, the function computes a default value. Within the body of the function, two quantities name
School: University Of Illinois, Urbana Champaign
Course: Calculus
Scripts and Functions You can see the file with type rank Here is the file. function r = rank(A,tol) % RANK Matrix rank. % RANK(A) provides an estimate of the number of linearly % independent rows or columns of a matrix A. % RANK(A,tol) is the number of s
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB r bar(r) Typing the statement magicrank causes MATLAB to execute the commands, compute the rank of the first 30 magic squares, and plot a bar graph of the result. After execution of the file is complete, the variables n and r rem
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB just assigns the names, one at time, to ans. But enclosing the expression in curly braces, cfw_S.name creates a 1-by-3 cell array containing the three names. ans = 'Ed Plum' 'Toni Miller' 'Jerry Garcia' And char(S.name) calls the
School: University Of Illinois, Urbana Champaign
Course: Calculus
Other Data Structures S(2).name = 'Toni Miller'; S(2).score = 91; S(2).grade = 'A-'; or, an entire element can be added with a single statement. S(3) = struct('name','Jerry Garcia',. 'score',70,'grade','C') Now the structure is large enough that only a su
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB There are enough blanks in each of the first four rows of S to make all the rows the same length. Alternatively, you can store the text in a cell array. For example, C = cfw_'A';'rolling';'stone';'gathers';'momentum.' is a 5-by-1
School: University Of Illinois, Urbana Champaign
Course: Calculus
Other Data Structures 2 3 61 60 6 7 57 9 55 54 12 13 51 50 16 17 47 46 20 21 43 42 24 40 26 27 37 36 30 31 33 32 34 35 29 28 38 39 25 41 23 22 44 45 19 18 48 49 15 14 52 53 11 10 56 8 58 59 5 4 62 63 1 . . 64 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 8 1 6 3
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB Internally, the characters are stored as numbers, but not in floating-point format. The statement a = double(s) converts the character array to a numeric matrix containing floating-point representations of the ASCII codes for eac
School: University Of Illinois, Urbana Champaign
Course: Calculus
Other Data Structures -? Concatenation with square brackets joins text variables together into larger strings. The statement h = [s, ' world'] joins the strings horizontally and produces h = Hello world The statement v = [s; 'world'] joins the strings v
School: University Of Illinois, Urbana Champaign
Course: Calculus
Other Data Structures and sum(M,2) is a 4-by-1-by-24 array containing 24 copies of the column vector 34 34 34 34 Finally, S = sum(M,3) adds the 24 matrices in the sequence. The result has size 4-by-4-by-1, so it looks like a 4-by-4 array. S = 204 204 204
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB Here are two important points to remember. First, to retrieve the contents of one of the cells, use subscripts in curly braces. For example, Ccfw_1 retrieves the magic square and Ccfw_3 is 16!. Second, cell arrays contain copies
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB stores the sequence of 24 magic squares in a three-dimensional array, M. The size of M is size(M) ans = 4 4 24 13 . . 16 3 2 16 11 13 10 3 117 13 14 7 8 14 12 106 14 15 12 9 7 6 1 4 14 15 1 4 10 12 15 6 9 12 8 3 121 10 1 6 3 11 8
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB The logic of the magic squares algorithm can also be described by switch (rem(n,4)=0) + (rem(n,2)=0) case 0 M = odd_magic(n) case 1 M = single_even_magic(n) case 2 M = double_even_magic(n) otherwise error('This is impossible') en
School: University Of Illinois, Urbana Champaign
Course: Calculus
5 Programming with MATLAB Flow Control MATLAB has several flow control constructs: if statements switch statements for loops while loops continue statements break statements if The if statement evaluates a logical expression and executes a group of
School: University Of Illinois, Urbana Champaign
Course: Calculus
Flow Control while The while loop repeats a group of statements an indefinite number of times under control of a logical condition. A matching end delineates the statements. Here is a complete program, illustrating while, if, else, and end, that uses inte
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 3. Solutions. Problem 1. Here we systematically develop the solution of the system (11.2.4), which is the formula for hi , that satises the recursion hi = phi+1 + qhi1 , h0 = 1. (1) a. Show that any constant solution hi = A satises (1).
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 5 Due Tuesday November 19, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon5s ol.pdf. Google automatic ally generates html vers ions of doc uments as we c rawl
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Fall 2011 Homework #5 (due Friday, October 7, by 3:00 p.m.) 1. Every month, the government of Neverland spends X million dollars purchasing guns and Y million dollars purchasing butter. Assume X and Y jointly follow a Bivariate Normal distributio
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 U3, G4 Fall 2011 Homework #1 (due Friday, September2, by 3:00 p.m.) 1. Below is a list of moment-generating functions. Provide (i) the values for mean and variance 2 , and (ii) P ( 1 X 2 ) for the random variable associated with each moment-gener
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics II
STAT 409 Fall 2011 Homework #11 (due Friday, December 2, by 4:00 p.m.) From the textbook: 8.7-1 ( ) 8.4-2 ( 8th edition ( 8.7-3 ( ) ) 8.4-4 ( ) 8.7-4 ( ) ) 8.7-6 ( 8.4-10 ( ) ) _ 8. In Neverland, annual income (in $) is distributed according to Gamma dist
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 1. Solutions. Problem 1. Prove Proposition 0.2.2. A guide to this problem: start with the open set S = (a, b), for example. First assume that a > , and show that the number a has the properties that it is a lower bound for S , and, for a
School: University Of Illinois, Urbana Champaign
STAT 409 Fall 2012 Homework #2 ( due Friday, September 14, by 4:00 p.m. ) 1. Let X 1 , X 2 , , X n be a random sample from the distribution with probability density function ( ) f X ( x ) = f X ( x ; ) = 2 + x 1 (1 x ) , a) 0 < x < 1, > 0. ~ Obtain the m
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 1 Due Tuesday September 10, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon1s ol.pdf. Google automatic ally generates html vers ions of doc uments as we c raw
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics II
MATH/STAT 409 Homework # 3 due 09/20/2013 1. Let > 0 and let X1 , X2 , . . . , Xn be a random sample of size n from a distribution with pdf f (x; ) = 43 x , 0 < x < . 4 (a) Find the MLE . (b) Is a consistent estimator? Justify your answer. (c) Is an unbia
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #10 (due Friday, April 6, by 3:00 p.m.) 1. Let X and Y have the joint p.d.f. f X Y ( x , y ) = 20 x 2 y 3 , 0 < x < 1, 0 < y < x, zero elsewhere. a) Find f X | Y ( x | y ). b) Find E ( X | Y = y ). c) Find f Y | X ( y | x ).
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 2 Due Tuesday September 24, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon2.pdf. Google automatic ally generates html vers ions of doc uments as we c rawl th
School: University Of Illinois, Urbana Champaign
Course: Engineering Applications Of Calculus
Math 231E. Fall 2013. HW 3 Solutions. Problem 1. Compute the following limits. Justify your answer. a. lim x2 6x + 4 x2 2x + 1 c. lim x1 (x 2)2 x2 6x + 4 b. lim x1 x2 d. lim x1 sin(x6 ) x e. lim x0 ex 1 x2 2x + 1 x1 (x 1)2 f. lim x0 sin(x) x ex 1 Solution
School: University Of Illinois, Urbana Champaign
Course: Intro Differential Equations
HW 71 1. Sec. 3.6: 3. We have x00 + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375; x0 (0) = 0: The characteristic equation is r2 + 100 = 0 =) r = mentary solution is 10i: The compli- xc (t) = c1 cos 10t + c2 sin 10t: r = 5i is not a root of the characteristi
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 2. Solutions. Problem 1. Let X, Y, Z, W be independent U (0, 1) random variables. Use a Monte Carlo method to compute E[XY 2 + eZ cos(W )]. How much computation should you do to be condent in your answer to three decimal places? (Turn in
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Prof. Rick Gorvett Fall, 2011 Homework Assignment # 8 (max. points = 10) Due at the beginning of class on Thursday, November 17, 201
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 409 Spring 2012 Homework #11 (due Thursday, April 12, by 4:30 p.m.) 1. 5.1-5 ( ) The p.d.f. of X is f X ( x ) = x 1 , 0 < x < 1, 0 < < . Let Y = 2 ln X. How is Y distributed? a) Determine the probability distribution of Y by finding the c.d.f. of Y F
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #6 1. 3.3-2 (a), 3.3-4 (a) ( , ) 2. 3.3-2 (b), 3.3-4 (b) ( , ) 3. 3.3-2 (c), 3.3-4 (c) ( , ) ( 4. 3.3-8 5. 3.3-24 (a),(b) ) ( ) 6. 3.4-4 ( ) 7. 3.4-8 ( ) 8. Suppose a random variable X has the following probability density fu
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #4 (due Friday, February 17, by 3:00 p.m.) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Sally sells seashells by the seashore. The daily sales X of
School: University Of Illinois, Urbana Champaign
Course: Alex
STAT 420 (10 points) (due Friday, November 7, by 3:00 p.m.) Homework #10 Fall 2008 1. Can a corporation's annual profit be predicted from information about the company's chief executive officer (CEO)? Forbes (May, 1999) presented data on company profit (
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #4 (due Friday, February 17, by 3:00 p.m.) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Sally sells seashells by the seashore. The daily sales X of
School: University Of Illinois, Urbana Champaign
Course: Engineering Applications Of Calculus
Math 231E. Fall 2013. HW 2 Solutions. Problem 1. Recall the Taylor series for ex at a = 0. a. Find the Taylor polynomial of degree 4 for f (x) = ex about the point a = 0. Solution: T4 (x) = 1 + x + x2 x3 x4 + +. 2 6 24 b. Use your answer to part (a) to es
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 409 Spring 2012 Homework #12 (due Friday, April 20, by 3:00 p.m.) 1 5. Let the joint probability density function for ( X , Y ) be f ( x, y ) = 1. x+ y 3 0 < x < 2, 0 < y < 1, , zero otherwise. a) Find the probability P ( X > Y ). b) Find the margina
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #5 (due Friday, February 24, by 3:00 p.m.) 1. Suppose a discrete random variable X has the following probability distribution: P( X = k ) = ( ln 2 ) k k! , k = 1, 2, 3, . Recall ( Homework #1 Problem 9 ): This is a valid prob
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #2 (10 points) (due Friday, February 3, by 3:00 p.m.) 1. A bank classifies borrowers as "high risk" or "low risk," and 16% of its loans are made to those in the "high risk" category. Of all the bank's loans, 5% are in default
School: University Of Illinois, Urbana Champaign
Course: Alex
STAT 420 Homework #4 (10 points) (due Friday, September 26, by 3:00 p.m.) Fall 2008 1. Hogg and Ledolter report on an engineer in a textile mill who studies the effects of temperature and time in a process involving dye on the brightness of a synthetic fa
School: University Of Illinois, Urbana Champaign
Course: Actuarial Risk Theory
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 476 / 567 Actuarial Risk Theory Prof. Rick Gorvett Fall, 2010 Homework Assignment # 4 (max. points = 8) Due at the beginning of class on Thursday, October
School: University Of Illinois, Urbana Champaign
STAT 409 Fall 2012 Homework #3 ( due Friday, September 21, by 4:00 p.m. ) 1. Let > 0 and let X 1 , X 2 , , X n be a random sample from the distribution with the probability density function f X (x) = f X ( x ; ) = a) x 2 e x , x > 0. Find the sufficient s
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2014 Homework #4 (due Friday, February 21, by 3:00 p.m.) No credit will be given without supporting work. 1 3. Alex sells Exciting World of Statistics videos over the phone to earn some extra cash during the economic crisis. Only 10% of al
School: University Of Illinois, Urbana Champaign
Course: Hw01&ans
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Actuarial Modeling Prof. Rick Gorvett Spring 2011 Homework Assignment # 1 (max. points = 10) Due at the beginning of class on Thursday, January 2
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2014 Homework #4 (due Friday, February 21, by 3:00 p.m.) No credit will be given without supporting work. 1 3. Alex sells Exciting World of Statistics videos over the phone to earn some extra cash during the economic crisis. Only 10% of al
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
SOLUTION TO HOMEWORK 11 MATH 335- Modern Algebra I The following result was proved in class and is used thoughout this solution. Proposition 1. If R is a ring and a, b R, then (i) a(b) = (a)b = ab and (ii) (a)(b) = ab. Problem 1 If R is a ring and a, b, c
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
SOLUTION TO HOMEWORK 4 MATH 335- Modern Algebra I Exercise 2.2.13 If an abelian group has an element a of order 4 and an element b of order 3, then it must also have elements of order 2 and 6. Proof: Let e denote the identity element of the group. Since a
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
SOLUTION TO HOMEWORK 9 MATH 335- Modern Algebra I Exercise 3.1.1 Let A and B be groups with identities eA and eB , respectively. Then A B is a group with identity (eA , eB ). Moreover, the inverse of an element (a, b) is (a1 , b1 ). Proof. Let (a, b), (a1
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
SOLUTION TO HOMEWORK 10 MATH 335- Modern Algebra I Problem 1 (a) Since the unique prime factorization of 1024 is 210 , the Structure Theorem for Finite Abelian Groups implies that all abelian groups of order 1024 are of the form Z2a1 Z2a2 Z2an , where a1
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
SOLUTION TO HOMEWORK 7 MATH 335- Modern Algebra I Exercise 2.4.7 Let : G H be a homomorphism of groups with kernel N . If a and x are elements of G, then the following are equivalent: (i) (a) = (x). (ii) a1 x N . (iii) aN = xN . Proof. (i) implies (ii): G
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
SOLUTION TO HOMEWORK 8 MATH 335- Modern Algebra I In this solution denotes Eulers totient function, unless otherwise stated. Exercise 1 The last digit of 712345 is 7. Proof. Note that the only positive integers that are less (or equal) and relatively prim
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
SOLUTION TO HOMEWORK 6 MATH 335- Modern Algebra I Exercise 1 Let n1 , n2 , ., nk be integers. Let H1 = cfw_n1 a1 + + nk ak | a1 , ., ak Z (the subgroup of Z generated by n1 , ., nk ) and H2 be the intersection of all subgroups of Z containing n1 , ., nk .
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
SOLUTION TO HOMEWORK 5 MATH 335- Modern Algebra I Exercise 1.6.4 Computing the greatest common divisor. (a) Successive divisions with remainder give 60 = 8 = 78+4 2 4. It follows that 4 = gcd(60, 8) and we can write 4 as a linear combination of 60 and 8.
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
SOLUTION TO HOMEWORK 3 MATH 335- Modern Algebra I Inversion Formula Remark: Suppose a and b are elements of a group G. When we write a = b1 , we mean a is the inverse of b in G, but we know that being a right inverse is equivalent to being a left inverse,
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
SOLUTIONS TO HOMEWORK 2 MATH 335- Modern Algebra I Computing Permutations Computations: 513642798x971265384=875124396. 318794256=(138596472). Let S=318794256. Given that S =(138596472) is a cycle, we can determine S 14 (1) by shifting 1 by 14 places to
School: University Of Illinois, Urbana Champaign
Course: Abstract Algebra I
SOLUTIONS TO HOMEWORK 1 MATH 355- Modern Algebra I Multiplication table of group of symmetries of the square Consider a square with vertices numbered as follows. Denote e the symmetry xing every vertex and say r is the symmetry that rotates the square cou
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #9: Spring 2015 Assigned April 13, due April 15 AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam LC Study S
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #1: Spring 2015 Assigned January 21, due January 28 AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam LC Stu
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #5: Spring 2015 Assigned February 18, due March 4 AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam LC Study
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #3: Spring 2015 Assigned February 4, due February 11 AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam LC St
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #4: Spring 2015 Assigned February 11, due February 18 AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam LC S
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #2: Spring 2015 Assigned January 28, due February 4 AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam LC Stu
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #6: Spring 2015 Assigned March 4, due March 11 AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam LC Study Su
School: University Of Illinois, Urbana Champaign
Course: Math
STAT 408 Spring 2015 A. Stepanov Homework #9 (due Friday, April 10, by 3:00 p.m.) Please include your name ( with your last name underlined ), your NetID, and your discussion section number at the top of the first page. No credit will be given without sup
School: University Of Illinois, Urbana Champaign
Course: Math
STAT 408 Spring 2015 A. Stepanov Homework #8 (due Friday, April 3, by 3:00 p.m.) Please include your name ( with your last name underlined ), your NetID, and your discussion section number at the top of the first page. No credit will be given without supp
School: University Of Illinois, Urbana Champaign
Course: Math
STAT 408 1. Practice Problems 14 Spring 2015 A. Stepanov Let X and Y have the joint probability density function x+4 y f X, Y ( x, y ) = 0 0 < y < x <1 otherwise a) Find P ( X > 4 Y ). b) Find the marginal probability density function of X, f X ( x ). c
School: University Of Illinois, Urbana Champaign
Course: Math
STAT 408 1. Spring 2015 A. Stepanov Practice Problems 13 Let X and Y have the joint probability density function f X , Y ( x, y ) = 1 x x > 1, 0 < y < , 1 x , zero elsewhere. / Let U = Y and V = Y X. Find the joint probability density function of ( U, V )
School: University Of Illinois, Urbana Champaign
Course: Math
STAT 408 1. Spring 2015 A. Stepanov Practice Problems 11 Let X and Y have the joint p.d.f. f X , Y ( x, y ) = C x 2 y 3 , 0 < x < 1, 0 < y < x, zero elsewhere. a) What must the value of C be so that f X , Y ( x, y ) is a valid joint p.d.f.? b) Find P ( X
School: University Of Illinois, Urbana Champaign
Course: Math
STAT 408 Homework #6 Spring 2015 A. Stepanov (due Friday, March 13, by 3:00 p.m.) Please include your name ( with your last name underlined ), your NetID, and your discussion section number at the top of the first page. No credit will be given without sup
School: University Of Illinois, Urbana Champaign
Course: Math
STAT 408 Spring 2015 A. Stepanov Examples for 5.2 (2) Let X and Y be continuous random variables with joint p.d.f. f ( x, y ) . Then Fact: f (x, w x ) dx f X + Y (w ) = (convolution) f (w y, y ) dy f X + Y (w) = Another Proof: Let V = X and W = X + Y. V
School: University Of Illinois, Urbana Champaign
Course: Math
STAT 408 0. Spring 2015 A. Stepanov Examples for 5.2 (1) Consider the following joint probability distribution p ( x, y ) of two random variables X and Y: y x 1 2 pX( x ) 1 0.15 0.10 0 0.25 2 0.25 0.30 0.20 0.75 pY( y ) a) 0 0.40 0.40 0.20 1.00 What is th
School: University Of Illinois, Urbana Champaign
Course: Math
STAT 408 Spring 2015 A. Stepanov Examples for 5.1 (2) Let X and Y be continuous random variables with joint p.d.f. f ( x, y ) . Then Fact: f X + Y (w ) = f (x, w x ) dx (convolution) f X + Y (w) = f (w y, y ) dy Proof: w x FX + Y (w) = f ( x, y ) dy dx
School: University Of Illinois, Urbana Champaign
Course: Math
STAT 408 Spring 2015 A. Stepanov Examples for 5.1 (2) Functions of One Random Variable Let X be a continuous random variable. Let Y = g ( X ). What is the probability distribution of Y ? Cumulative Distribution Function approach: FY( y ) = P( Y y ) = P( g
School: University Of Illinois, Urbana Champaign
Course: Math
STAT 408 1. Spring 2015 A. Stepanov Examples for 5.1 (1) Consider two continuous random variables X and Y with joint p.d.f. f X, Y ( x, y ) = 60 x 2 y, x > 0, y > 0, x + y < 1, zero elsewhere. Consider W = X + Y. Find the p.d.f. of W, f W ( w ). w w x F W
School: University Of Illinois, Urbana Champaign
Course: Calculus
MATH 220 Midterm 3 Review This is a sheet of things I think are important to know. Material on the test is not limited to items on this sheet. The test will cover sections 3.10, 4.2, 4.8-4.9, 5.1 - 5.5, 6.1-6.3, 6.5, 7.2. 1. Find the following antiderivat
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 1 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (2 points) Given two nonzero vectors u and v which are not parallel, are u v and v u? 2. (2 points) D
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 3 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Find any three dierent parametrizations of the graph y = x2 . 2. (3 points) Find the equat
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 2 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Find the area of the triangle with vertices P (1, 0, 2), Q(0, 0, 3) and R(7, 4, 3). 2. (3
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 4 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) If z = ln(x100 + y 100 ) where x = s100 t100 and y = s100 + t100 , nd z/s and z/t. 2. (3 p
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 5 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Write T if the statement is true and F if it is false. If your answer is F, then briey exp
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 6 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (5 points) Evaluate the following integral by reversing the order of integration. 1 0 1 x ex/y dydx (
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 8 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (2 points) Write T if the following statement is true and F if it is false. If your answer is F, then
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 9 Spring 2012 Name 1. (2 points) What is the denition of the Jacobian of the transformation T given by u = g(x, y) and v = f (x, y)? 2. (4 points)Use the given transformation to evaluate the following integral. (x2 xy + y 2 )dA
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD5) Quiz 10 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) Write T if the statement is true and F if the statement is false. If it is false, then ex
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD4) Quiz 11 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Use Greens Theorem to evaluate the line integral. F = yi xj clockwise around the unit cir
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD4) Quiz 10 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (1 point) True or False: If vector eld. c Fdr = 0 where C is a closed path , then F is not a conserv
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD4) Quiz 9 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (2 points) Sketch the vector eld F(x,y)=yj 2. (4 points) Let E be the trapezoid with verities (8,0),(
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD4) Quiz 6 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Find the volume of the solid beneath the paraboloid f (x, y) = 12 x2 2y 2 and above the re
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD4) Quiz 3 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. Do one out of the two 1 point problems 1. (1 point) True or False: < cos(3t), sin(3t) > and < cos(5t 1),
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD4) Quiz 5 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (1 point) True or False: Every function has at least one local minimum. 2. (4 points) Find the critic
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD4) Quiz 1 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (2 points) Suppose u = 2i + 1j + 3k and v = j + 2k. Determine |u 3v|. 2. (2 points) Determine a unit
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD4) Quiz 2 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Find the area of the triangle with vertices P (2, 1, 2), Q(3, 1, 1) and R(1, 2, 1). 2. (4
School: University Of Illinois, Urbana Champaign
Fifth Homework Set Solutions Chapter 4 Problem 4.35 Let X be the win/loss after one game. Then P cfw_X = 1.1 = 20 45 = 4 , 9 and P cfw_X = 1 = (a) E [X] = 1.1 4 9 5 9 2(5) 2 (10) 2 = 5 . 9 1 = 15 . 5 (b) Var (X) = E [X 2 ] E [X]2 = 1.21 4 + 9 9 1 225 =
School: University Of Illinois, Urbana Champaign
Practise problems 1) What is the probability of at least three of a kind in poker? Solution: Among 5 cards we can only have three of a kind of one kind. Thus we have 13 choices for a kind. Then we may have four of this kind: 52 4 = 48 possibilities. Then
School: University Of Illinois, Urbana Champaign
Sixth Homework Set Solutions Chapter 4 Problem 4.72 Let A be the stronger team. P (A wins in i games) = for i = 4, . . . , 7. Hence 7 P (A wins best-of-seven series) = i=4 i1 i4 0.6i 0.4i4 , i1 0.64 0.4i4 = 0.7102. i4 Similarly, 3 P (A wins best-of-three
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (sections DD2 and DD7) Quiz 2 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Find the area of the triangle with vertices P (1, 1, 1), Q(2, 1, 3) and R(3, 4, 3
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD7) Quiz 1 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (2 points) Suppose u = 2i + 4j + 4k and v = j + k. Determine |2u 3v|. 2. (2 points) Determine a unit
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (sections DD2 and DD7) Quiz 3 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) The curves r1 (s) = 3(s 1), 2(s 1), 5(s 1)2 and r2 (t) = sin (t), sin (2t), t int
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD7) Quiz 4 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 20 minutes for this quiz. 1. (4 points total) Let f (x, y) = xy (a) (2 points) Find x2 y 2 . f. (b) (2 points) Find a vector that
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (sections DD7 and DD2) Quiz 10 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 20 minutes for this quiz. 1. (6 points total)(Its the simple things.) Let C be the helix parameterized by r(t) = (cos(t)
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (sections DD2 and DD7) Quiz 11 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 20 minutes for this quiz. 1. (4 points)(The George Green Lantern) One day, George Green was writing a mathematical treat
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD6) Quiz 1 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (2 points) Suppose u = i 2j + 2k and v = j k. Determine |3u 2v|. 2. (2 points) Determine a vector of
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD6) Quiz 2 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Find the area of the triangle with vertices P (1, 0, 2), Q(0, 0, 3) and R(5, 2, 3). 2. (4
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD8) Quiz 3 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) The curves r1 (s) = 3(s 1), 2(s 1), 5(s 1)2 and r2 (t) = sin (t), sin (2t), t intersect at
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD6) Quiz 4 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) Find a unit vector normal to the surface given by z = x2 y 2 + y + 1 at the point (0, 0, 1). Spring 20
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD6) Quiz 5 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (5 points) The function f (x, y) = x4 + 4xy + xy 2 has 3 critical points. Calculate the three critica
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD6) Quiz 9 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) Compute the gradient vector eld of f , where f = arctan (x/y). Spring 2012 2. (6 points) Let R be a pa
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD6) Quiz 10 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) Let f (x, y, z) = xy xz, and C be a curve lie in the intersection of two surfaces y = x2
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD6) Quiz 8 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) Let the point P = (1, 3, 2 3) be given in rectangular coordinate. Express this point in
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD6) Quiz 11 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) Compute C xe2x dx + (x4 + 2x2 y 2 + y 4 )dy, where C is the positively oriented boundary
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD8) Quiz 9 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) Compute the gradient vector eld of f , where f = arctan (x/y). Spring 2012 2. (6 points) Let R be a pa
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD8) Quiz 10 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) Let f (x, y, z) = xy xz, and C be a curve lie in the intersection of two surfaces y = x2
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD8) Quiz 11 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) Compute C xe2x dx + (x4 + 2x2 y 2 + y 4 )dy, where C is the positively oriented boundary
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD8) Quiz 4 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) Find a unit vector normal to the surface given by z = x2 y 2 + y + 1 at the point (0, 0, 1). Spring 20
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD6) Quiz 6 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Find the volume of the solid beneath the paraboloid f (x, y) = 12 x2 2y 2 and above the re
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD8) Quiz 5 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (5 points) The function f (x, y) = x4 + 4xy + xy 2 has 3 critical points. Calculate the three critica
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD8) Quiz 3 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) The curves r1 (s) = 3(s 1), 2(s 1), 5(s 1)2 and r2 (t) = sin (t), sin (2t), t intersect at
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD8) Quiz 8 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (4 points) Let the point P = (1, 3, 2 3) be given in rectangular coordinate. Express this point in
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD8) Quiz 2 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (3 points) Find the area of the triangle with vertices P (0, 1, 2), Q(0, 0, 3) and R(5, 2, 4). 2. (4
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 (section DD8) Quiz 1 Spring 2012 Name No calculators allowed. Show sucient work to justify each answer. You have 15 minutes for this quiz. 1. (2 points) Suppose u = i + 2j + 2k and v = j k. Determine |2u 3v|. 2. (2 points) Determine a unit vec
School: University Of Illinois, Urbana Champaign
Course: Actuarial Modeling
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Actuarial Modeling Prof. Rick Gorvett Spring, 2015 Sample Exam C Problems Kaplan-Meier Product-Limit Estimator
School: University Of Illinois, Urbana Champaign
Course: Actuarial Modeling
Exercises from Loss Models, 3rd Edition fourth edition Chapters 12-15 10-13 Exercise 10.7 Exercise12.7 Exercise 11.5 Exercise 13.5 Exercise 13.8 Exercise 11.8 Exercise14.6 Exercise 12.6 Exercise 14.8 Exercise 12.8 Exercise 14.23 Exercise 13.8 Exercise 15.
School: University Of Illinois, Urbana Champaign
Course: Actuarial Modeling
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Actuarial Modeling Prof. Rick Gorvett Spring, 2015 Sample Exam C Problems Cumulative Hazard Rate and Nelson-alen Estimator
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 286 E1 The University of Illinois at Urbana-Champaign Department of Mathematics Title of Course: Intro to Differential Equations Plus Room and time: MTWR 1:00-1:50pm in 103 Transportation Building. Instructor: Bogdan Udrea Office location: 241 Illini
School: University Of Illinois, Urbana Champaign
Course: College Algebra
MATH 115 PREPARATION FOR CALCULUS FALL 2013 Instructor Office E-mail Lecture A1 8am 100 Gregory Hall Lecture D1 11am 114 DKH Jennifer McNeilly 121 Altgeld Hall jrmcneil@illinois.edu Lecture X1 Noon 217 Noyes Lab Theodore Molla 226 Illini Hall molla@illino
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Syllabus for the Midterm Exam on February 23 * Systems of linear equations and their applications (Sections 1.1, 1.2) * Gaussian elimination, row-echelon form (Section 1.2) * Matrix operations (Sections 1.3, 1.4, 1.5) * Nonsingular matrices, computing
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
MATH416AbstractLinearAlgebra I. GeneralInformation Instructor:BenjaminWyser ContactInfo: TimeandPlace:MWF9:00am 9:50am,141AltgeldHall Email:bwyser@illinois.edu OfficePhone:(217)3000363 OfficeLocation:222AIlliniHall OfficeHours:MWF1:002:00,orby appointment
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/567: ACTUARIAL THEORY II/ TOPICS IN ACTUARIAL THEORY I SPRING 2012 -INSTRUCTOR: Name: Office: Office phone number: E-mail address: Paul H. Johnson, Jr. 361 Altgeld Hall (217)-244-5517 pjohnson@illinois.edu Website: http:/www.math.uiuc.edu/~pjohns
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 286 Sections D1 & X1 Introduction to Differential Equations Plus Spring 2014 Course Information Sheet INSTRUCTOR: Michael Brannan CONTACT INFORMATION: Ofce: 376 Altgeld Hall. Email: mbrannan@illinois.edu COURSE WEB PAGE: http:/www.math.uiuc.edu/~mbra
School: University Of Illinois, Urbana Champaign
Course: Actuarial Problem Solving
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 370 (Section Z) Actuarial Problem Solving Spring 2014 245 Altgeld Hall 7:00-8:50 pm Tuesday Starting February 4, 2014 12 Lectures Sarah Manuel Office Hours
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 / MATH 408 Spring 2014 Actuarial Statistics I Monday, Wednesday, Friday Instructor: 9:00 9:50 a.m. 101 Armory Alex Stepanov Office: 101-A Illini Hall E-mail: stepanov@illinois.edu Office hours: ph.: 265-6550 Monday 3:30 4:30 p.m., Thursday 1:30 2
School: University Of Illinois, Urbana Champaign
Course: Elementary Linear Algebra
MATH 125: Calculus with Analytic Geometry II Instructor: Farhan Abedin Email: abedinf@uw.edu Oce: Padelford C-404 Oce Hours: TA: Neil Goldberg Email: neilrg@uw.edu Oce: Padelford C-34 Oce Hours: Text: Calculus, James Stewart, 7th Edition. MATH 125 Materia
School: University Of Illinois, Urbana Champaign
Math 231 B1 Summer 2012 Instructor: Vyron Vellis Oce: B3 Coble Hall, 217-244-3288 Oce hours: M 2-2:50PM, W 3-3:50PM B3 Coble Hall or by appointment Homepage: http : /www.math.uiuc.edu/ vellis1/math 231 sum2012.html E-mail: vellis1@illinois.edu Textbook: C
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 Calculus III Section AL1 at MWF 9:00-9:50 in 314 Altgeld Hall Section CL1 at MWF 2:00-2:50 in 314 Altgeld Hall Spring 2010 Instructor: Tom Carty Oce: 121 Altgeld Hall Oce Phone: 265-6205 email: carty@illinois.edu Oce Hours: To Be Determined Websi
School: University Of Illinois, Urbana Champaign
Syllabus of the course MATH 482 LINEAR PROGRAMMING AND COMBINATORIAL OPTIMIZATION This is a course on mathematical aspects of problems in linear and integral optimization that are relevant in computer science and operation research. It is based on the boo
School: University Of Illinois, Urbana Champaign
Math 482 (Linear Programming and Combinatorial Optimization): (Spring 2011) Instructor: Alexander Yong ayong@math.uiuc.edu Lectures: MWF 1:00-1:50pm 141 Altgeld Office Hours: By appointment only, but in particular, I'm free MF 2:00-3:00pm (right after cla
School: University Of Illinois, Urbana Champaign
Math 482 (Linear Programming and Combinatorial Optimization): (Spring 2011) Instructor: Alexander Yong ayong@math.uiuc.edu Lectures: MWF 1:00-1:50pm 141 Altgeld Office Hours: By appointment only, but in particular, I'm free MF 2:00-3:00pm (right after cla
School: University Of Illinois, Urbana Champaign
Course: Differential Geometry Of Curves And Surfaces
DEP 3053 Syllabus, 1/8/2012 DEP 3053 DEVELOPMENTAL PSYCHOLOGY, LIFESPAN, SPRING 2012 Section # 0069 Instructor: Office Hours: Office: Phone: Email: ILAN SHRIRA Wednesday, 3-5pm; also available by appointment Room 273, Psychology Building 273-0166 ilans@uf
School: University Of Illinois, Urbana Champaign
Course: MLC
MATH 471: ACTUARIAL THEORY I FALL 2010 -INSTRUCTOR: Name: Office: Office phone number: E-mail address: Paul H. Johnson, Jr. 361 Altgeld Hall (217)-244-5517 pjohnson@illinois.edu Website: http:/www.math.uiuc.edu/~pjohnson/ Office Hours: Monday 1:00-2:00pm,