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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: Actuarial Modeling
Standard Normal Distribution Values x 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 0.5
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
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: 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 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: 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: Actuarial Modeling
Standard Normal Distribution Values x 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 0.5
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
Ruled surfaces A surface is called ruled if it is swept out by moving a line in space. That is, there exiss a family of lines so that each point of the surface lies on exactly one line from this family (so, the lines are either parallel, or skew). The lin
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
THE TNB FRAME, THE CURVATURE, ETC. Throughout, we consider a spacecurve r = r(t). t |r (u)| du (length of the arc of the curve Let s be the arclength parameter: s = a ds with a u t). Then = |r (t)|. dt dr r The unit tangent vector: T = = . ds |r | The
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Integrals as General & Particular Solutions dy = f (x) dx General Solution: y(x) = f (x) dx + C Particular Solution: dy = f (x), dx y(x0 ) = y0 dy Examples: 1) dx = (x 2)2 ; y(2) = 1; 2) dy dy 10 = x2 +1 ; y(0) = 0; 3) dx = xex ; y(0) = 1; dx p. 2/3 Inte
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Review of MATH 385, Section D2 The nal will cover: (*=the content you should know to understand other subject, but no problem is directly for this subject) Chapter 1 (30pts) (except Exact equations) : The order of dierential equations, particular solution
School: University Of Illinois, Urbana Champaign
Solutions to Midterm 2 Review Problems for Math 231 Page 1 Solutions to Midterm 2 Review Problems for Math 231 Page 2 Solutions to Midterm 2 Review Problems for Math 231 Page 3 Solutions to Midterm 2 Review Problems for Math 231 Page 4 Solutions to Midter
School: University Of Illinois, Urbana Champaign
Math 231 Fall 2014. Worksheet 12. 10/23/14
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Math 231. Fall 2014. More review problems for Midterm 2. Some of these are old exam problems. This is neither a comprehensive list of review problems nor a complete study guide. Solutions will be posted. The problems will not be collected. 2 1. Consider t
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Group: Name: Math 231 A. Fall, 2013. Worksheet 15. 11/12/13 You will need Taylors Theorem, which says that f (x) = TN (x) + RN (x), where TN (x) is the degree N Taylor polynomial for f at a, and the remainder RN (x) equals RN (x) = f (N +1) (z) (x (N + 1)
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Group: Name: Math 231 A. Fall, 2013. Worksheet 13. 11/5/13 1. Augustin-Jean Fresnel (1788-1827) was an engineer, mathematician and the French commissioner of lighthouses. He is famous for his work in optics and for developing the Fresnel lens. Originally
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Course: Solution
Math 231E. Fall 2012. Solutions to limit review problems. For each of the following, set up and solve an inequality which veries the asserted limit. 1. lim 4x 3 = 5 x2 Start with |4x 3 5| < and simplify to |4x 8| < 4|x 2| < |x 2| < /4. So = /4 works. Form
School: University Of Illinois, Urbana Champaign
Course: Solution
Math 231E. Fall 2012. A few review problems. 1. Calculate the limit, or show that it does not exist. ex1 sin(x 1) cos(x 1) x1 (ln(x)2 lim 2. Find the Taylor series for f (x) = ln(cos(x2 ) about 0, to fourth degree. Then dierentiate the series to evaluate
School: University Of Illinois, Urbana Champaign
Course: Solution
Math 231E. Fall 2012. limit review problems. Not to turn in. For each of the following, set up and solve an inequality which veries the asserted limit. 1. lim 4x 3 = 5 x2 2. lim x2 = 0 x0 3. lim x2 = 16 x4 4. (1 + h)2 1 lim =2 h0 h
School: University Of Illinois, Urbana Champaign
Course: Solution
4. Find the volume of the solid obtained by rotating the region bounded by the curves x=1 about the y-axis. 10. Find the volume of the solid obtained by rotating the region bounded by the curves and y=1 about the x-axis. y=x 2 , x= y , y=0, and x=0, 15. F
School: University Of Illinois, Urbana Champaign
Course: Solution
MATH 231E. Practice Final Exam Solutions. There are 5 problems all worth equal points. You must not communicate with other students during this test. No books, notes, calculators, or electronic devices allowed. This is a 20 minute exam. Do not turn t
School: University Of Illinois, Urbana Champaign
Course: Calculus I
The Fundamental Theorem of Calculus 1 The Fundamental Theorem of Calculus 1.1 Part I 1.2 Part II 2 Proofs 2.1 Proof of Part II of FTC Complete the steps below to prove the second part of the Fundamental Theorem of Calculus. (Note, this only holds for a <
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Properties of Summation Notation and the Definite Integral 1 1.1 Summation Properties Examples of summation notation n i f (i) = f (1) + 2f (2) + 3f (x) + + (n 1)f (n 1) + nf (n). (1) i=1 5 i2 = 1 + 4 + 9 + 16 + 25. (2) i=1 5 i=0 1.2 1 2 i =1+ 1 1 1 1 1 +
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Schedule for Math 221.AL1 Fall 2014 (This schedule is subject to change.) All section numbers correspond to Stewarts Calculus: Early Transcendentals (7e). W = Group Worksheet. Q = Quiz. Week Date Topics 1 Monday, August 25 2.1 Tuesday, August 26 W1 Wednes
School: University Of Illinois, Urbana Champaign
Course: Calculus I
How to do your best in Calculus To do well in a course, you must develop eective learning habits. This list is just a few. Make sure you have mastered the pre-requisites. You wont do well in Calculus I without being good in Algebra and Trigonometry. Like
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Sections covered from Stewarts Calculus: Early Transcendentals (7e) in Math 221 - Fall 2014 Chapter 2: Limits and Derivatives 2.1 The Tangent and Velocity Problems 2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.5 Continuity 2.6
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Additional Exercises for Math 221 All section numbers correspond to Stewarts Calculus: Early Transcendentals (7e). Chapter 1 1.1: 1-2, 3, 7-10, 14, 21, 25, 27-30, 31-37, 38, 39-50, 58, 69-70, 71, 73-78, 79-80. 1.2: 1-2, 6, 16, 19-20. 1.3: 3, 6-7, 9-24, 2
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Midterm 2: Time: 9:00-9:50 AM on October 27th, 2014 Place: 066 Library (the standard classroom) Sections: 3.5 - 3.11, 4.1 - 4.5 and 4.7 - 4.9 Topics: 1. (5 points) From Exam I 2. (13 points) Curve Sketching 3. (14 points) 3.5 - 3.11 material (but not rela
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Lesson 8b: Optimization 1 The idea behind optimization We recently saw how we could use knowledge about functions to determine precisely when a function has a maximum or a minimum. In this section, we will see applications of using these skills. For examp
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Taalman-62052 book 400 December 31, 2003 10:56 CHAPTER 5 Polynomial Functions much as possible. Check your answers by multiplying out your factorization. 79. f (x) = x 3 2x 2 5x + 6 80. f (x) = 3x 3 8x 2 + 5x 2 81. f (x) = x 3 + 4x 2 11x + 6 82. f (x) = x
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Inverse Functions What you may remember from high school. Example 1: Find the inverse function of f (x) := and f 1 . 1 . Determine the domain and range of f x2 This technique will help us determine the inverse function, but what exactly is an inverse func
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Logarithmic Functions Consider any basic exponential function: To nd an inverse function algebraically, we switch the role of x and y and solve for y. Denition: For b > 0 and b = 1, the base b logarithmic function is dened by Remarks: We will begin with s
School: University Of Illinois, Urbana Champaign
Course: College Algebra
1 1.1 Function Review Function Review Discussion Question: What do you remember about functions? Denition: A function, f dened on a subset of real numbers, D is a rule that assigns to each value, , in D exactly one value, denoted f (). The set D is calle
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Sequences and Limits Motivational Example: Repeated Drug Doses Suppose a doctor orders you to take 16mg of a drug every 12 hours for 10 days. Assume your liver and kidneys remove 25% of the drug from your bloodstream every 12 hours. What happens to the dr
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Prep for Exam 2 Topics: Arithmetic and Geometric Sequences - denitions, generating functions/formulas, limits Series - denition, nite arithmetic and geometric series formulas, summation notation, innite series denition, theorems related to innite series
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Finding Zeros of Polynomial Functions Some reminders. Theorem: The Rational Root Theorem p Let be a rational number written in fully reduced form. Consider the polynomial equation q cn xn + cn1 xn1 + . . . + c1 x + c0 = 0 p is a zero (or q a solution) of
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 8: Ratemaking II September 18, 2014 1 Last Time Ratemaking I Overall concept Two foundational techniques Pure premium method L
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 9: Risk Classification September 30, 2014 1 Agenda Ratemaking relativities Risk classification 2 Ratemaking Relativities T
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 11: Individual Risk Rating October 2, 2014 1 Agenda Individual Risk Rating Types of plans Prospective rating Retrospectiv
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 5: Loss Reserving II September 9, 2014 1 Agenda Review of basic loss development technique and essential metrics / quantities Oth
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 4: Loss Reserving I September 4, 2014 1 Agenda Purpose of Loss Reserving Loss data Types of reserves Key dates Types of
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 7: Ratemaking I September 16, 2014 1 Agenda Ratemaking I Overall concept Two basic techniques Pure premium method Loss ratio m
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 6: Loss Reserving III September 11, 2014 1 Agenda Accounting issues Statement of Loss Reserving Principles 2 Accounting Issues Ra
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479/568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 3: Economics and Insurance Markets September 2, 2014 1 Last Time Insurance contracts Lines of business Insurability Etc 2 C
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 1: Introduction and Overview August 26, 2014 Agenda Syllabus Moi The actuarial profession The casualty actuarial professi
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 2: Risks and Risk Theory August 28, 2014 What Did We Discuss Last Time? What an actuary is, in words and numbers What actua
School: University Of Illinois, Urbana Champaign
Course: Calculus For Business I
Section 5.3 continued Integration Rules for Denite Integrals Let f and g be any functions continuous on a x b. Then b b kf (x)dx = k (1) Constant multiple rule: a b (2) Sum rule: g (x)dx a b b f (x)dx [f (x) f (x)]dx = g (x)dx a a a a b f (x)dx + a b (3)
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
| r srv s g kv 8 s r jeyvw4faaefCGyeaiuiIs wx!x o arvvs9!uEseA4yavuyyfyrGx Qynavu~vvsehaiv ywEsfCeavuinaCF wr x P s w x w | S r 8 s g x x sv u |yxay~eyvwaaG!daIiiG!veavuisA!x vw4!a!veavuisA!eleiu WEX2(811y)Ehv w r sd v sr x oud
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review Important Geometric Examples Representing linear maps by matrices Nonstandard Bases MATH 415 Lecture 17 Monday, 2 March 2015 Additional Problems Review Important Geometric Examples Representing linear maps by matrices Textbook reading: Chapter 2.6
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review Inner Product and Distances Inner Product and Angles MATH 415 Lecture 19 Fri, 6 March 2015 Orthogonal vectors Review Inner Product and Distances Textbook reading: Ch 3.1 Inner Product and Angles Orthogonal vectors Review Inner Product and Distances
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review The inverse of a matrix Composition rules An algorithm for computing the inverse matrix Math 415 - Lecture 8 February 6th, 2015 Review The inverse of a matrix Textbook: Chapter 1.6 Composition rules An algorithm for computing the inverse matrix Rev
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
MATH 415 Lecture 18 Wednesday, 4 March 2015 Textbook reading: Chapter 2.6 Textbook reading: Chapter 2.6 Suggested practice exercises: same as lecture 16 Review A map T : V W between vector spaces is linear if A map T : V W between vector spaces is linear
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
MATH 415 Lecture 14 23rd February 2015 Textbook reading: Chapter 2.3 Textbook reading: Chapter 2.3 Suggested practice exercises: Chapter 2.3 Exercise 1, 2, 3, 5, 6, 9, 11, 16, 19, 20, 22, 27. Textbook reading: Chapter 2.3 Suggested practice exercises: Cha
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
MATH 415 Lecture 12 16 February 2015 Textbook reading: Section 2.3 Textbook reading: Section 2.3 Suggested practice exercises: Section 2.3: 1, 2, 5 Textbook reading: Section 2.3 Suggested practice exercises: Section 2.3: 1, 2, 5 Khan Academy video: Textbo
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review Warmup MATH 415 Lecture 15 23 February 2015 Bases for Column and Null Spaces Review Warmup Textbook reading: 2.4 Bases for Column and Null Spaces Review Warmup Bases for Column and Null Spaces Textbook reading: 2.4 Suggested practice exercises: Cha
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review - Elementary matrices Triangular matrices Row exchanges Math 415 - Lecture 7 February 4th, 2015 Applications Practice problems Review - Elementary matrices Triangular matrices Textbook: Chapter 1.5 Row exchanges Applications Practice problems Revie
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
MATH 415 Lecture 13 18 February 2015 Review Review A vector space is a set V of vectors which can be added and scaled (without leaving the space!); subject to the usual rules. Review A vector space is a set V of vectors which can be added and scaled (with
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review Column Spaces MATH 415 Lecture 11 13 February 2015 Col(A) and solutions to Ax = b Review Column Spaces Textbook: Chapter 2.1, 2.2. Col(A) and solutions to Ax = b Review Column Spaces Col(A) and solutions to Ax = b Textbook: Chapter 2.1, 2.2. Sugges
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Elementary matrices Math 415 - Lecture 6 February 2nd, 2015 Elementary matrices Textbook: Chapter 1.4, 1.5 Elementary matrices Textbook: Chapter 1.4, 1.5 Suggested Practice Exercise: Chapter 1.4 Exercise 22, 27, Chapter 1.5: 4, 5, 11, 23, 29 Elementary ma
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Vector Spaces and Subspaces Vector Space Examples MATH 415 Lecture 9 9 February 2015 Subspaces Vector Spaces and Subspaces Textbook: Chapter 2.1. Vector Space Examples Subspaces Vector Spaces and Subspaces Vector Space Examples Textbook: Chapter 2.1. Sugg
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
MATH 415 Lecture 10 11 February 2015 Textbook: Chapter 2.1, 2.2. Textbook: Chapter 2.1, 2.2. Suggested practice exercises: Chapter 2.1: 3, 21, 28. Chapter 2.2: 33 and additional exercises at the end of this lecture. Textbook: Chapter 2.1, 2.2. Suggested p
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review Rank and Dimensions The Four Fundamental Subpaces Coordinates MATH 415 Lecture 16 Friday, 27 February 2015 Linear Transformations Review Rank and Dimensions The Four Fundamental Subpaces Textbook: Chapter 2.4, 2.6 Coordinates Linear Transformations
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review: Solution of linear systems Math 415 - Lecture 3 January 26th, 2015 Review: Solution of linear systems Textbook: Chapter 1.2 Review: Solution of linear systems Textbook: Chapter 1.2 Suggested Practice Exercise: Read section 1.2, do problem 1.3:9 (d
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Matrix operations Math 415 - Lecture 5 January 30th, 2015 Matrix operations Textbook: Chapter 1.4 Matrix operations Textbook: Chapter 1.4 Suggested Practice Exercise: Chapter 1.4 Exercise 1, 2, 10, 12, 13, 21, 30, 34, 45, Matrix operations Textbook: Chapt
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Row Reduction and Echelon Forms Pivots Math 415 - Lecture 2 January 23, 2015 Solution of linear systems Row Reduction and Echelon Forms Pivots Solution of linear systems Textbook: Chapter 1.3, Chapter 2.2 (just the pages 78 and 79) Row Reduction and Echel
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Review The row and column picture Math 415 - Lecture 4 January 28th, 2015 Matrix operations Review The row and column picture Textbook: Chapter 1.3, 1.4 Matrix operations Review The row and column picture Matrix operations Textbook: Chapter 1.3, 1.4 Sugge
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Systems of Linear Equations Two Fundamental Questions (Existence and Uniqueness) Math 415 - Lecture 1 January 22, 2015 Row Reduction and Echelon Forms Systems of Linear Equations Two Fundamental Questions (Existence and Uniqueness) Row Reduction and Echel
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
The n-dimensional space Rn Basic facts: the n-dimensional space Rn is a generalization of R2 (the plane) or R3 (the 3-dimensional space) to the n-variable case. Formally Rn is the set of ordered n-tuples of real numbers: (x1 , . . . , xn ). We can identif
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
Determinants, cross products, and triple products 1. Determinants. a1 a2 = a1 b2 a2 b1 . Geometrically, this determinant represents the signed b1 b2 area of the parallelogram formed by the vectors a1 , a2 and b1 , b2 . The sign is positive if we need to r
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
FORMULA SHEET FOR MIDTERM 1 Trigonometric identities: sin2 x+cos2 x = 1, tan2 x+1 = sec2 x, sin 2x = 2 sin x cos x, 1 1 cos2 x = (1 + cos 2x), sin2 x = (1 cos 2x), sec d = ln | sec + tan | + C. 2 2 Exponential and logarithmic functions: ln(ab) = ln a + ln
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 II
Math 231 Practice Final Instructions: This is a practice exam. Please treat it as a regular exam: sit down and take it in 3 hours without interruption and without reference to the textbook or to the class notes. After this you may want to spend some time
School: University Of Illinois, Urbana Champaign
Course: Calculus II
Group: Name: Math 231 A. Fall, 2014. Worksheet 1. 8/26/14 These problems review some material from Calculus I. You will work on them in groups today, and turn the papers in at the end of the section. Solutions will be posted. 1 1. (a) Sketch the graph of
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Math 286 G1 - Midterm 2 Practice Clearly, it is too long for a single exam. Take the rst 7 for timed trial. 1. For the unforced oscillation equation mx (t) + cx (t) + kx(t) = 0 . Derive the criteria that distinguishes under-, critical-, over- damped cases
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Math 286 G1 - Midterm 2 Practice Clearly, it is too long for a single exam. Take the rst 7 for timed trial. 1. For the unforced oscillation equation mx (t) + cx (t) + kx(t) = 0 . Derive the criteria that distinguishes under-, critical-, over- damped cases
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 285 F1 G1 Midterm 3, Form A April 18, 2014 NAME (please print legibly): Your University ID Number: Please complete all 5 questions in the space provided. No paper of your own is allowed. You may use the backs of the pages for extra space. You may a
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 285 F1 G1 Midterm 3, Form B April 18, 2014 NAME (please print legibly): Your University ID Number: Please complete all 5 questions in the space provided. No paper of your own is allowed. You may use the backs of the pages for extra space. You may a
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 285 Parrish Name Make-Up Exam 2 November 11th , 2010 You will have 50 minutes to complete the exam. You may use the back of each page as scratch paper. If you run out of space for a response, you may continue on the back of the page. Material pre
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 285 Parrish Name Exam 2 November 1st , 2010 You will have 50 minutes to complete the exam. You may use the back of each page as scratch paper. If you run out of space for a response, you may continue on the back of the page. Material presented on
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 285 F1 G1 Midterm 2 March 21, 2014 NAME (please print legibly): Your University ID Number: Please complete all 5 questions in the space provided. No paper of your own is allowed. You may use the backs of the pages for extra space. You may also ask
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Math 285 - Intro Dierential Equations Spring 2011, section G1 Midterm 2, Friday April 15 Name: Solutions No calculators, electronic devices, books, or notes may be used. Show your work. No credit for answers without justication. All Fourier series must be
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Math 285 Practice Exam 2 Show all your work. Present your solutions clearly. No credit will be given for unjustied answers. Calculators are not allowed. 1. (a) Are the functions x, ex , and xex linearly dependent? (b) Is it possible that these functions s
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Math 285 - Intro Dierential Equations Spring 2011, section G1 Midterm 2, Friday April 15 Name: No calculators, electronic devices, books, or notes may be used. Show your work. No credit for answers without justication. All Fourier series must be computed.
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
NAME: Math 285 Midterm 2 practice Total points: 100. Please explain all answers. Calculators, computers, books and notes are not allowed. Suggestion: even if you cannot complete a problem, write out the part of the solution you know. You can get partial c
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Math 285 Midterm 2 practice solutions Problem 1: We know the Fourier Series of a constant is just the same constant, so the F.S. of 2 is just 2. We now calculate the F.S. of t, which is an odd function, so we only need to calculate the Fourier series coec
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 285 F1 G1 Midterm 1 February 21, 2014 NAME (please print legibly): Your University ID Number: Please complete all 5 questions in the space provided. No paper of your own is allowed. You may use the backs of the pages for extra space. You may also a
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 286 E1 Midterm 1 Form A February 19, 2015 NAME (please print legibly): Your University ID Number: Please complete all 5 questions in the space provided. No paper of your own is allowed. You may use the backs of the pages for extra space. You may al
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 286 E1 Midterm 1 Form B February 19, 2015 NAME (please print legibly): Your University ID Number: Please complete all 5 questions in the space provided. No paper of your own is allowed. You may use the backs of the pages for extra space. You may al
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 285 G1 Final Exam October 16, 2014 NAME (please print legibly): Your University ID Number: Please complete all 8 questions in the space provided. No paper of your own is allowed. You may use the backs of the pages for extra space. You may also ask
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 286 H1 Final Practice Answers NAME (please print legibly): Your University ID Number: Please complete all 8 questions in the space provided. No paper of your own is allowed. You may use the backs of the pages for extra space. You may also ask me fo
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
NAME: Math 285 Final exam practice Total points: 100. Please show the work you did to get the answers. Calculators, computers, books and notes are not allowed. Suggestion: even if you cannot complete a problem, write out the part of the solution you know.
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Math 285 Final practice solutions Problem 1: This is a constant coecients equation, so we look for a solution of the form y = erx . The characteristic equation for r is: r5 4 r4 + 4 r3 = 0 which has solutions r = 0 (three times), and r = 2 (twice). The ge
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 286 H1 Final Exam December 15, 2014 NAME (please print legibly): Your University ID Number: Please complete all 9 questions in the space provided. No paper of your own is allowed. You may use the backs of the pages for extra space. You may also ask
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 1 September 3, 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. Pa
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 Fall 2013 Exam 1 September 26, 2013 Solutions 1. (6 points) Let U = cfw_1, 2, 3, 4, 5, 6, 7, 8, A = cfw_1, 2, 3, 5, and B = cfw_2, 4, 5, 6. Compute the following sets. (a) Ac Solution: Ac = cfw_4, 6, 7, 8 (b) A [ B Solution: A [ B = cfw_1, 2, 3,
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 3 September 17, 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. P
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 4 September 24, 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. P
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 2 September 10, 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. P
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Math 286 G1 Midterm 1 Practice Solution 1. (a) order 1, nonlinear, NA (b) order 2, nonlinear, non-homogeneous (c) order 1, linear, homogeneous (d) order 4, linear, homogeneous (e) order 2, nonlinear, NA 2. Refer the the book. 3. (a) H = e P (x)dx (b) H =
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Math 286 G1 Midterm 1 This is a mock-up exam for the real one. The actual exam will provide enough space for your writing. Here, we are saving trees in Brazil. 1. [?pt] Determine the orders of the following dierential equations. Also nd if they are linear
School: University Of Illinois, Urbana Champaign
Old exam questions from Math 231 Math 231 AL1. Exam 3. April 21, 2011 -Name: There are eight multiple choice problems series six 4. a) Use the binomial theorem to nd the MacLaurin worth for points each. Mark answers on Scantron forms in pencil. No partia
School: University Of Illinois, Urbana Champaign
Course: MATH
PENGUMUMAN BAGI MAHASISWA BARU UNIVERSITAS INTERNASIONAL BATAM ANGKATAN 2014/2015 1. Kegiatan Program Pengenalan Mahasiswa Baru Tahun 2014 bertema Reach to the Top Jadwal kegiatan mahasiswa baru UIB angkatan 2014/2015 sebagai berikut : AGUSTUS SEPTEMBER M
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
NAME 3. (20 points) Find the distance of the vector z to the Spancfw_v1 , v2 . 1 1 1 1 0 1 v1 = v2 = z= 0 0 1 1 1 2 NAME 6. (20 points) Solve the following linear system. If an exact solution does not exist, nd a least squares solution. x1 + x2 x
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
NAME MATH 410 - E13, Test 1, Fall 2014 September 24, 2014 Calculators, books, notes and extra papers are not allowed on this test Please show all your work and explain all answers to qualify for full credit 1. (20 points) Solve the following linear system
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
Name: _ UIN: _ Version B UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Instructor: Jianan Xu Spring, 2011 Exam # 2 (6 Questions + 1 Bonus Question; Max possible points = 100+15) Wednesday, April 6, 2011 Y
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
Name: _ UIN: _ Version A UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Instructor: Jianan Xu Spring, 2011 Exam # 2 (6 Questions + 1 Bonus Question; Max possible points = 100+15) Wednesday, April 6, 2011 Y
School: University Of Illinois, Urbana Champaign
Course: Calculus
Math 220 (section AD?) Quiz 10 Fall 2012 Name You have 15 minutes No calculators x2 1. (3 points) Suppose w(x) = Show sucient work (t 4)(t + 1)6 dt. Determine all intervals upon which the 10 function w(x) is increasing. 2. (2 points) Precisely state Th
School: University Of Illinois, Urbana Champaign
Course: Calculus
AL1 (MWF 8:00-8:50) AL2 (MWF 9:00-9:50) MATH 220 AL3 (MWF 1:00-1:50) Test 2 Fall 2014 Name NetID Sit in your assigned seat (circled below). Circle your TA discussion section. Do not open this test booklet until I say START. Turn o all electronic devices 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
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: Honors Linear Algebra
Math 416 D13, HW 1 Solution 1. Write z = rei . Then z 3 = i r3 e3i = e 2 i r3 = 1 & 3 = + 2k, k Z 2 2k r=1 & = + ,k Z 6 3 When k = 0, = ; when k = 1, = + 2 = 5 ; and when k = 2, 6 6 3 6 = + 4 = 3 . These 3 values repeat as k ranges over Z. Hence, 6 3
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Math 416 D13, HW 3 Solution by Yongfei Ci 1. Treil 6.1 We must show Av1 , Av2 , . . . , Avn are generating and linearly independent. Let w W . Since A is an isomorphism, v V such that Av = w. Write v = n ai vi for some ai R, i = 1, . . . , n. Then i=1 w =
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Pre-class worksheet due Monday, Aug 29 (Solutions). 1. For each of the following statements indicate if it is true or false: (a) The vectors v1 = (1, 2, 4)T , v2 = (2, 4, 8)T are linearly independent in R3 . Solution. False. Indeed 2v1 + 1 v2 = 0 is a non
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Pre-class worksheet due Wednesday, September 7 (Solutions). 1. For each of the following statements indicate if it is true or false: x xy )= is linear. y x + 2y 1 1 2 Solution. False. E.g. 2f ( )=2 = , but 1 3 6 1 2 4 1 1 f (2 ) = f( )= so that 2f ( ) = f
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Pre-class worksheet due Friday, Aug 26 (solutions). 1. Compute the following complex numbers (that is, represent each of them in the form x + yi where x, y R): (a) (2 + i) (1 3i) = (2 + i)(1 + 3i) = 2 3 + i(1 + 6) = 5 + 5i. (b) 1 1 2i 1 2i 1 2i 1 2 = = =
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Pre-class worksheet due Friday, September 2 (Solutions). 1. For each of the following statements indicate if it is true or false: (a) Any basis of a vector space V is a generating system for V . Answer: Yes, this is true. This statement is a part of Propo
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Pre-class worksheet due Friday, September 9 (Solutions). 1. Write down the matrix of a linear trasformation T : R2 R3 given by the formula f ([x, y]T ) = [2x y, x + 5y, x]T ). Answer: We have: 2 1 AT = 1 5 . 1 0 2. Let T1 : V W and T2 : W U be R-linear ma
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Pre-class worksheet due Monday, September 12 (Solutions). 1. Give an example of two matrices A, B M2,2 (R) such that (AB)T = AT B T . Solution. 1 2 1 0 and B = . 0 1 1 1 3 2 3 1 Then AB = and (AB)T = . On the other hand, 1 1 2 1 For example, take A = AT B
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Pre-class worksheet due Monday, September 19 (Solutions). 1. Let V0 V be a subspace of a vector space V . Is it true that V \ V0 = cfw_v V : v V0 is a subspace of V ? Answer: No, this statement is not true. Indeed, a subspace must always contain 0, so th
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Pre-class worksheet due Wednesday, September 21 (Solutions) 1. For the system x1 + 2x2 2x4 = 1 x1 + 2x2 + 4x3 + x4 = 7 write down the augmented matrix of this system. Solution. The augmented matrix of this system is: 1 2 0 4 1 1 2 4 1 7 2. For the system
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Pre-class worksheet due Friday, September 23 (Solutions). PRINT YOUR NAME: 1. For the system x1 + 2x2 2x4 = 1 x + 2x2 + 4x3 + x4 = 7 1 8x2 + 8x3 x4 = 0 (a) Take the system into a row-echelon form by applying row operations (b) Write down the full solutio
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Pre-class worksheet due Wednesday, September 14 (Solutions). 1. Find a left inverse of the matrix A = 1 and a right inverse of the 1 matrix B = 1 2 . 1 = 1 so that 1/5 4/5 is a left inverse of A. 1 2/3 2/3 is a right inverse of the = 1 so that 1 2 1/3 1/3
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
Pre-class worksheet due Monday, September 26 (Solutions). 1. For each of the following statements indicate whether it is true or false: (1) If W, V are vector spaces over R such that dim(V ) = 2 and dim(W ) = 3 then V is not isomorphic to W . (2) If W is
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
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: Actuarial Modeling
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Actuarial Modeling Prof. Rick Gorvett Old Actuarial Exam Problems Deductibles and Policy Limits A jewelry store has obtained two separate
School: University Of Illinois, Urbana Champaign
Course: Actuarial Modeling
For Aid in Preparing for Exam # 1, Math 478 / 568, Spring 2015 UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Actuarial Modeling Prof. Rick Gorvett Spring, 2011 Exam # 1 (17 Problems Max possi
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,