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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
(* 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: 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
(* 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: Finite Mathematics
Math 124 Exam 2 Review. This is a start, but is not a complete review. (1) Given (2, 0) and (5, 3) (a) Find the slope. (b) Graph the line. (2) Given the following demand and supply equations algebraically nd the equilibrium point. D(x) = 3x + 2 S(x) = 2x
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
Course: Applied Linear Algebra
Linear Algebra and Its Applications Fourth Edition Gilbert Strang x y z Ax y Ay b b b 0 0 z Az 0 Contents Preface iv 1 . . . . . . . . 1 1 4 13 21 36 50 66 72 . . . . . . . 77 77 86 103 115 128 140 154 . . . . . . 159 159 171 180 195 211 221 2 3 Matrices
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
Errata for Actuarial Mathematics for Life Contingent Risks David C M Dickson, Mary R Hardy, Howard R Waters Note: These errata refer to the rst printing of Actuarial Mathematics for Life Contingent Risks. Some corrections may have been incorporated in sub
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Examples for 03/28/2012 4.3 Conditional Distributions and Expectations. 1. Consider the following joint probability distribution p ( x, y ) of two random variables X and Y: y x 0 1 2 pX( x ) 1 0.15 0.10 0 0.25 2 0.25 0.30 0.20 0.75 pY
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Examples for 04/02/2012 Functions of a Random Variable Example 1: y = x2 pY( y ) = pX( y ) 1 4 9 16 0.2 0.4 0.3 0.1 x pX( x ) 1 2 3 4 0.2 0.4 0.3 0.1 x pX( x ) y pY( y ) 2 0.2 0 p X ( 0 ) = 0.4 0 0.4 4 p X ( 2 ) + p X ( 2 ) = 0.5 2 0.
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 2. Spring 2012 Examples for 03/30/2012 Let the joint probability density function for ( X , Y ) be 2 f (x, y ) = 60 x y 0 x 1, 0 y 1, x + y 1 Recall: 0 otherwise f X ( x ) = 30 x 2 ( 1 x ) 2 , E( X ) = 1 , 2 9 , 252 Var ( X ) = f Y ( y ) = 20 y (
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: 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
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: 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: 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: 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 Modeling
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Actuarial Modeling Prof. Rick Gorvett Spring 2012 Project: Data Analysis and Write-Up Due At or Before the Final Exam at 1:30 pm, Wednesday, May
School: University Of Illinois, Urbana Champaign
Course: Differential Equations
Math 441 Syllabus - Spring 2014 Text: Elementary Dierential Equations and Boundary Value Problems, John Wiley & Sons, Inc., by Boyce and DiPrima 9th edition. Instructor: Nikolaos Tzirakis Introduction/Motivation/Terminology (2 Lectures) How dierential e
School: University Of Illinois, Urbana Champaign
Course: Calculus II
Math 231: Calculus II Study guide for midterm 2 (mastery exam) The second midterm will cover material from chapters 7 and 8. The goal of the exam is to test basic skills and problem solving WITHOUT THE USE OF A CALCULATOR. The following is a list of
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Short study guide for nal, math 286, Fall 2008 Note that the nal is comprehensive, so study all your study guides and past exams and exam solution sheets. You may also be asked questions relating to the IODE project! Here are some sample solved probl
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
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
(* 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: 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
(* 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 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: 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
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: 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: 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 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: 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: 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 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: 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: 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: 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
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 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: 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 #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: 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 #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: 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: 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: 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: 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: 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
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 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
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: 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 Linear Algebra
Strang-5060 book May 5, 2005 13:52 69 Chapter 2 Vector Spaces 2.1 VECTOR SPACES AND SUBSPACES Elimination can simplify, one entry at a time, the linear system Ax = b. Fortunately it also simplies the theory. The basic questions of existence and uniqueness
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
4 Growth Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 2 Publisher: Math Everywhere, Inc. Version 6.0 1.09 Parametric Plotting BASICS -4 B.1) Parametric plots in two dimensions: Circular parameters A handy way to plot the circle x2 + y 2 = 9
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
You can plot a surface z = f @x, yD like this: In[1]:= Accumulation Clear@f, x, yD; f@x_, y_D = 3.1 x2 + 2.3 y2 ; 88a, b<, 8c, d< = 88- 2, 3<, 8- 1, 4<; surfaceplot = Plot3D@f@x, yD, 8x, a, b<, 8y, c, d<D; Authors: Bill Davis, Horacio Porta and Jerry Uhl
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Strang-5060 book May 5, 2005 13:52 69 Chapter 2 Vector Spaces 2.1 VECTOR SPACES AND SUBSPACES Elimination can simplify, one entry at a time, the linear system Ax = b. Fortunately it also simplies the theory. The basic questions of existence and uniqueness
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Examples for 08/22/2011 random variables Fall 2011 discrete probability mass function p.m.f. continuous probability density function p.d.f. p( x ) = P ( X = x ) x 0 p( x ) 1 f( x ) x f( x ) 0 =1 p(x ) = 1 all x f (x) d x - cumulative distributi
School: University Of Illinois, Urbana Champaign
Course: Intro Differential Equations
Notes on Diffy Qs Differential Equations for Engineers by Ji Lebl r July 16, 2010 2 A Typeset in LTEX. Copyright c 20082010 Ji Lebl r This work is licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License. To view
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Section 4.2 The Mean Value Theorem 2010 Kiryl Tsishchanka The Mean Value Theorem THEOREM (The Extreme Value Theorem): If f is continuous on a closed interval [a, b], then f attains an absolute maximum value f (c) and an absolute minimum value f (d) at som
School: University Of Illinois, Urbana Champaign
Course: Calculus I
A DIAGRAM SKETCH OF THE FUNDAMENTAL THEOREM OF CALCULUS The Fundamental Theorem of Calculus states that if f f is continuous on [a, b], then d dx Denition of Derivative. By the denition of the derivative, d dx since x x f (t)dt a = f (x). f (t)dt a = lim
School: University Of Illinois, Urbana Champaign
Course: Calculus I
A WRITTEN SKETCH OF THE FUNDAMENTAL THEOREM OF CALCULUS The Fundamental Theorem of Calculus states that if f is continuous on [a, b], then d dx x f (t)dt a = f (x). Denition of Derivative. By the denition of the derivative, d dx x f (t)dt a = lim x+h f (t
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 Exam 2 Review. This is a start, but is not a complete review. (1) Given (2, 0) and (5, 3) (a) Find the slope. (b) Graph the line. (2) Given the following demand and supply equations algebraically nd the equilibrium point. D(x) = 3x + 2 S(x) = 2x
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
MATH 416 HOMEWORK ASSIGNMENT #7: DUE WEDNESDAY, NOVEMBER 13TH (1) Section 6.1: 2, 3, 11, 17, 18, 20, 26 (2) Section 6.2: 2 (a-f only), 3, 4, 6, 9, 14, 18 1
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
Course: Applied Linear Algebra
Linear Algebra and Its Applications Fourth Edition Gilbert Strang x y z Ax y Ay b b b 0 0 z Az 0 Contents Preface iv 1 . . . . . . . . 1 1 4 13 21 36 50 66 72 . . . . . . . 77 77 86 103 115 128 140 154 . . . . . . 159 159 171 180 195 211 221 2 3 Matrices
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
Errata for Actuarial Mathematics for Life Contingent Risks David C M Dickson, Mary R Hardy, Howard R Waters Note: These errata refer to the rst printing of Actuarial Mathematics for Life Contingent Risks. Some corrections may have been incorporated in sub
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Examples for 03/28/2012 4.3 Conditional Distributions and Expectations. 1. Consider the following joint probability distribution p ( x, y ) of two random variables X and Y: y x 0 1 2 pX( x ) 1 0.15 0.10 0 0.25 2 0.25 0.30 0.20 0.75 pY
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Examples for 04/02/2012 Functions of a Random Variable Example 1: y = x2 pY( y ) = pX( y ) 1 4 9 16 0.2 0.4 0.3 0.1 x pX( x ) 1 2 3 4 0.2 0.4 0.3 0.1 x pX( x ) y pY( y ) 2 0.2 0 p X ( 0 ) = 0.4 0 0.4 4 p X ( 2 ) + p X ( 2 ) = 0.5 2 0.
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 2. Spring 2012 Examples for 03/30/2012 Let the joint probability density function for ( X , Y ) be 2 f (x, y ) = 60 x y 0 x 1, 0 y 1, x + y 1 Recall: 0 otherwise f X ( x ) = 30 x 2 ( 1 x ) 2 , E( X ) = 1 , 2 9 , 252 Var ( X ) = f Y ( y ) = 20 y (
School: University Of Illinois, Urbana Champaign
Course: Methods Of Applied Statistics
1. Consider the population of high school graduates who were admitted to a particular university during a ten-year time period and who completed at least the first year of coursework after being admitted. We are interested in investigating how well Y, the
School: University Of Illinois, Urbana Champaign
Course: Methods Of Applied Statistics
STAT 420 1. Summer 2012 Practice Problems 2 Suppose that the amount of beer a person has consumed ( X ) and the persons blood alcohol level ( Y ) in a certain bar follow a bivariate normal distribution with X = 60 oz, a) X = 15 oz, Y = 0.072, Y = 0.02
School: University Of Illinois, Urbana Champaign
Course: Methods Of Applied Statistics
STAT 420 Spring 2012 Examples #2 X1 X2 X= . X n 1 2 E( X) = = . n n-dimensional random vector 11 12 21 22 = . . n1 n 2 . 1n . 2n . . nn ij = Cov ( Xi , Xj ) = E [ ( X ) ( X )' ] symmetric, positive-definite Multivariate Normal Distr
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/MATH 567: Actuarial Theory II/Topics in Actuarial Theory I Chapter 7: Lecture Examples 1. Consider a fully discrete whole life insurance of 1 on (35): (i) lx = 100 - x for 0 x 100 (ii) i = 0.06 (a) Calculate the level annual benet premium. (b) De
School: University Of Illinois, Urbana Champaign
Course: Actuarial Modeling
INVITED PAPER COOPERATIVE GAME THEORY AND ITS INSURANCE APPLICATIONS BY J E A N L E M A I R E Wharton School University of Pennsylvania, USA ABSTRACT This survey paper presents the basic concepts of cooperative game theory, at an elementary level. Five ex
School: University Of Illinois, Urbana Champaign
Course: Actuarial Modeling
Game Theory .net - News stories by field of study Educators Students Professionals Geeks News : story cache Game theory in the popular press. Can the Risk of Terrorism Be Calculated By Insurers? Game Theory Might Do It Bush Expected to Prod Congress To Ac
School: University Of Illinois, Urbana Champaign
Course: Actuarial Risk Theory
January 8, 2008 09:31 780 n41-main Sheet number 810 Page number 780 black w Interest Rate Models The Behavior of Bonds and Interest Rates Before discussing how a bond market-maker would delta-hedge, we rst need to specify how bonds behave. Suppose we try
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, 2011 MFE Sample Exam and Spring 2007 Problems (from SOA) Option Greeks, Delta, Gamma
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, 2012 MFE Old and Sample Exam Problems (from SOA) Volatility, Black-Scholes, and misc.
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, 2012 Sample MFE Exam Problems (from SOA) Put-Call Parity, Binomial Pricing, and Real Probabilities
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, 2012 Sample MFE Exam Problems (from SOA) Put-Call Parity and Binomial Pricing
School: University Of Illinois, Urbana Champaign
Course: Actuarial Risk Theory
Volume XCII, Part 2 No. 177 PROCEEDINGS November 13, 14, 15, 16, 2005 MODELING FINANCIAL SCENARIOS: A FRAMEWORK FOR THE ACTUARIAL PROFESSION KEVIN C. AHLGRIM, STEPHEN P. DARCY, AND RICHARD W. GORVETT Abstract This paper summarizes the research project on
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 15 Mon, 02/17/2014 Inhomogeneous linear DEs Recall that a linear DE is one of the form y (n) + pn1(x) y (n1) + + p1(x)y + p0(x)y = f (x). d Writing12 D = dx and setting L 6 D n + pn1(x) Dn1 + + p1(x)D + p0(x), this DE takes the concise f
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 14 Wed, 02/12/2014 Review Basic understanding DEs and IVPs visualization of rst-order DEs via slope elds existence and uniqueness Basic modeling population models mixing problems modeling simple motions Solving techniques linear DEs with
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 13 Tue, 02/11/2014 Review. linear independence Fix some a I. Note that y(x) = C1 y1(x) + + Cnyn(x) is the general solution of a HLDE8 of order n if and only if we can solve for all initial values y(a) = b0, y (a) = b1, , y (n1)(a) = bn1.
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 12 Mon, 02/10/2014 Review. complex numbers Example 51. Here is another way, to look at Eulers identity eix = cos (x) + i sin (x). For this identity to make sense, one needs to somehow characterize the exponential function on the left-han
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 11 Thu, 02/06/2014 Review. homogeneous linear DEs with constant coecients Example 43. Find the general solution of y y 5y 3y = 0. Solution. The characteristic equation is r 3 r 2 5r 3 = (r 3)(r + 1)2. This corresponds to the solutions y1
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 9 Tue, 02/04/2014 Review. population models Example 35. Short outbreaks of diseases among a population of constant size N . Model the population as consisting of S(t) susceptible, I(t) infected and R(t) recovered individuals (N = S(t) +
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 10 Wed, 02/05/2014 Example 38. Solve the IVP y + 7y + 14y + 8y = 0 with y(0) = 1, y (0) = 0, y (0) = 1. Solution. Last time, we found that the DE has the general solution y(x) = Aex + Be 2x + Ce 4x. y(x) = Aex + B e2x + Ce4x, y(0) = A +
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 8 Mon, 02/03/2014 Population models To model a population, let P (t) be its size at time t. (t), (t): birth and death rate [# of births/deaths (per unit of population per unit of time) at time t] P = (t)P (t)t (t)P (t)t dP = (t) (t)P dt
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 7 Thu, 01/30/2014 Review. Useful substitutions Example 27. Solve (x y)y = x + y. Solution. y y Divide the DE by x to get 1 x y = 1 + x . This is a homogeneous equation! 1+u 1 + u2 We therefore substitute u = to nd the new DE xu + u = 1 u
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 1 Tue, 01/21/2014 Very basic examples of dierential equations 2 2 Example 1. If y(x) = ex then y (x) = 2xex = 2xy(x). 2 We say that y(x) = ex is a solution to the dierential equation (DE) y = 2xy. Example 2. If y(x) = sin (3x) then y (x)
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 5 Tue, 01/28/2014 Example 20. Solve y = ky. Solution. Write as dy dx 1 dy = k dx (note that y hence |y | = ek x+C . Since = ky, then we just lost the solution y = 0). Integrating gives ln |y| = kx + C, the RHS is never zero, y = ek x+C =
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 2 Wed, 01/22/2014 1 Review. Verify that x(t) = c kt is a one-parameter family of solutions to Solution. = kx2. k x (t) = (c k t)2 = kx(t)2 Solve the IVP: Solution. dx dt dx dt = kx2, x(0) = 2. [What about x(0) = 0, instead?] 7 1 1 ! =c c
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 4 Mon, 01/27/2014 Review. Existence and uniqueness of solutions Example 15. Discuss the IVP xy = 2y, y(a) = b. 3 Solution. f (x, y First, write as y = f (x, y) with f (x, y) = 2y/x. We compute y) = 2/x. Therefore, both f (x, y) and x 0.
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 6 Wed, 01/29/2014 Review. linear rst-order equations Example 25. A tank contains 20gal of pure water. It is lled with brine (containing 2lb/gal salt) at a rate of 3gal/min. At the same time, well-mixed solution ows out at a rate of 2gal/
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 3 Thu, 01/23/2014 Understanding DEs without solving them Slope elds, or sketching solutions Example 9. Consider the DE y = x/y. Lets pick a point, say, (1, 2). If a solution y(x) is passing through that point, then its slope has to be y
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: MLC
MATH 471: Actuarial Theory I Midterm #1 October 6, 2010 General Information: 1) There are 9 problems for a total of 50 points. 2) You have between 7:00-8:50pm to write the midterm. 3) You may refer to both sides of one 3in X 5in notecard. 4) You may use a
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Section 4.2 The Mean Value Theorem 2010 Kiryl Tsishchanka The Mean Value Theorem THEOREM (The Extreme Value Theorem): If f is continuous on a closed interval [a, b], then f attains an absolute maximum value f (c) and an absolute minimum value f (d) at som
School: University Of Illinois, Urbana Champaign
Course: Calculus I
A DIAGRAM SKETCH OF THE FUNDAMENTAL THEOREM OF CALCULUS The Fundamental Theorem of Calculus states that if f f is continuous on [a, b], then d dx Denition of Derivative. By the denition of the derivative, d dx since x x f (t)dt a = f (x). f (t)dt a = lim
School: University Of Illinois, Urbana Champaign
Course: Calculus I
A WRITTEN SKETCH OF THE FUNDAMENTAL THEOREM OF CALCULUS The Fundamental Theorem of Calculus states that if f is continuous on [a, b], then d dx x f (t)dt a = f (x). Denition of Derivative. By the denition of the derivative, d dx x f (t)dt a = lim x+h f (t
School: University Of Illinois, Urbana Champaign
Course: Calculus I
The following are the questions from the Final given by Randy McCarthy for Math 221 in Fall of 2012. It is provided so that students can get some sense of length and diculty of McCarthys nals in 221, but the specic format and question selection is likely
School: University Of Illinois, Urbana Champaign
Course: Calculus I
The following are the questions use for a version of Exam III in Math 221 section AL1 in Fall 2012 (McCarthys section). It me be rather dierent than the one to be used in sections AL1 and BL1 for Fall 2013 but it is being provided for those curious about
School: University Of Illinois, Urbana Champaign
Course: Calculus I
The following are the questions used for a version of Exam II in Math 221 section AL1 in Fall 2012 (McCarthys section). It may be rather dierent than the one to be used in sections AL1 and BL1 for Fall 2013 but it is being provided for those curious about
School: University Of Illinois, Urbana Champaign
Course: Calculus I
1. (8 points) The half-life of cesium-137 is 30 years. Suppose we have a 70 -mg sample. Find the mass that remains after t years. 2. (8 points) Find the absolute maximum and absolute minimum values of f (x) = x3 3x2 9x + 1 on [2, 1] 3. (16 points, 3/3/5/5
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
MATH 416 HOMEWORK ASSIGNMENT #5: DUE WEDNESDAY, OCTOBER 16TH Recall that a matrix A is similar to a matrix B if and only if there is an invertible matrix P such that P 1 AP = B. (1) Show that similarity is an equivalence relation on the set of n n matrice
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
MATH 416 FINAL EXAM TOPICS FOR SECTIONS 6.3, 6.4, 6.5, AND 6.8 Denitions to know (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Adjoint of a linear operator Normal operator Self-adjoint operator Unitary operator, unitary matrix Orthogonal operator, orthogonal m
School: University Of Illinois, Urbana Champaign
Course: Honors Linear Algebra
MATH 416 QUIZ 3 1. Let f : R3 R3 be the linear transformation R3 R3 given (with respect to the standard basis) by the matrix 2 1 1 A = 1 4 1 . 1 3 0 Find the matrix of f with respect to the basis 0 1 1 B = 1 , 1 , 0 . 1 1 1 That is, nd RepB,B (f ).
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Test 1 Practice Questions (First set) (1) Consider the following linear system and answer the questions. = 2 x+yz 3x 5y + 13z = 18 x 2y + 5z = k (a) (b) (c) (d) Write the augmented matrix. Find the augmented matrix. For which values of k the system is c
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Test 1 Practice Questions (Second set) (1) Determine which of the following transformation are linear. For those, write the associated matrix. (If you can write a transformation as a matrix multiplication then it is automatically linear, no further comput
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Math 415 Old Exam # 1 1. (12 points) (a) Find LU an 3 3 A= 6 factorization of the matrix 2 0 1 2 7 5 2 5 1 2 0 1 the augmented matrix. (b) If a matrix B has the factorization LU 2 2 5 1 0 0 2 8 7 18 = 4 1 0 0 B= 0 3 7 0 3 1 0 T solve Bx = 3 10 7 without r
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Math 415 S13 Midterm I (Version B) February 14, 2013 . . Name & UIN#: This is a closed-book, closed-notes exam. No electronic aids are allowed. Read each question carefully. Unless otherwise stated you need to justify your answer. Do not use results not
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Math 415 Exam # 1 Solutions 1. (15 points) Let LD22 denote the set of lower triangular 2 2 matrices, i.e. the set of matrices of the form A= x1 0 x2 x3 (a) Show that LD22 is a subspace of M22 Solution: (5 points) aA + bB = a x1 0 x2 x3 +b y1 0 y2 y3 = ax1
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
MATH 415: SOLUTIONS FOR MIDTERM 1 1 (8 points): Consider the following transformations from R2 to R2 . Determine which of these transformations is linear. If a transformation is not linear, explain why. If it is linear, determine the transformation matrix
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
5.1 O rth ogonal Projections and O rth o n o rm al Bases 199 In the case of meat consumption and cancer, we find that 4182.9 r ^ - % 0.9782. 198.53 21.539 The angle between the two deviation vectors is arccos(r) 0.21 (radians) 12 . Note that the length of
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
110 CHAPTER 3 Subspaces of R n and T heir D im ensions EXERCISES 3.1 GOAL Use the concepts o f the image and the kernel o f a linear transformation (ora matrix). Express the image and the kernel o f any matrix as the span o f some vectors. Use kernel and
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Math 415 S13 Midterm II (Version A) March 14, 2013 . . Name & UI#: This is a closed-book, closed-notes exam. No electronic aids are allowed. Read each question carefully. Unless otherwise stated you need to justify your answer. Do not use results not pr
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: 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: 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: 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 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: 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: 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 #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: 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
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 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
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: Finite Mathematics
J ~c G. I G. Each o~ ~ a 4-tu~(cfw_)./~/()W,th a. l:f/l] ellh~r evtn or odd I b l':rtYl fl e( ?i15 or j S,C ~in~ the (0/ rY" of the card J d(avl I a1 cl d Vi nj tII.e (on k 0 f fN ud d(auY] . WIn 1VJt nUMW of r()~t I~. I ~ P (5, ) t r Pr (5: t f P(
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
r:> 1 - I 0-4-.2_ G. 4. b ,_ _,(~ ) _ _-'( 1. I B) o_,_ ?r ~ (_o. b )(~g ) ~ l(Jc;)(o-~1+ (o.? )(o. ~) + (o . l )(0.4 ~- b_ C_ ) - Pr (ll \B ) :. _j_ _ b( c_o .!;) ( o. 2>) (O.b )(0-8' ) + ( 0 -?>)(0 .3) + ( 0.1 )(0.4 ) - ( c_ _ ?r- ( 1tr I B J -: -( G I
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on October 17th and 18th 1. Let L : R2 R3 be a linear transformation such that 2 3 1 8 , L 0 0 . L = = 0 1 4 1 What is L 2 1 ? 2. Let T : R2 R4 be the linear transformations with 5 1 1 T = 0 , T 1 1 1
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on October 10th and 11th 1. a) For which values of h is v3 in the span of v1 and v2 ? b) For which values of h is cfw_v1 , v2 , v3 linearly dependent? 1 2 2 (i) v1 = 5 , v2 = 10 , v3 = 9 , 3 6 h 7 2 1 3
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on October 10th and 11th 1. a) For which values of h is v3 in the span of v1 and v2 ? b) For which values of h is cfw_v1 , v2 , v3 linearly dependent? 1 2 2 (i) v1 = 5 , v2 = 10 , v3 = 9 , 3 6 h 7 2 1 3
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on October 3rd and 4th 1. Find an explicit description of Nul A, where A= 1 3 5 0 0 1 4 2 . x1 x Solution: We rst bring the augmented matrix of the equation A 2 = 0 into x3 x4 reduced echelon form: 1 3
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on October 3rd and 4th 1. Find an explicit description of Nul A, where A= 1 3 5 0 0 1 4 2 . 1 3 1 2 1 2 6 4 8 and b = 3 . Find all solutions to the equation Ax = b. 2. Let A = 0 0 2 4 1 1
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Preparation problems for the discussion sections on September 26th and 27th 1. Solve the practice exam for Midterm 1. See separate le. 2. Determine which of the following sets are subspaces and give reasons: a (a) W1 = cfw_ b : a 2b = c, 4a + 2c = 1, c
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 2012 Project: Data Analysis and Write-Up Due At or Before the Final Exam at 1:30 pm, Wednesday, May
School: University Of Illinois, Urbana Champaign
Course: Differential Equations
Math 441 Syllabus - Spring 2014 Text: Elementary Dierential Equations and Boundary Value Problems, John Wiley & Sons, Inc., by Boyce and DiPrima 9th edition. Instructor: Nikolaos Tzirakis Introduction/Motivation/Terminology (2 Lectures) How dierential e
School: University Of Illinois, Urbana Champaign
Course: Calculus II
Math 231: Calculus II Study guide for midterm 2 (mastery exam) The second midterm will cover material from chapters 7 and 8. The goal of the exam is to test basic skills and problem solving WITHOUT THE USE OF A CALCULATOR. The following is a list of
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Short study guide for nal, math 286, Fall 2008 Note that the nal is comprehensive, so study all your study guides and past exams and exam solution sheets. You may also be asked questions relating to the IODE project! Here are some sample solved probl
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,