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School: UCLA
Course: Linear Algebra And Applications
Name: Student ID: Prof. Alan J. Laub Section: 1 April 29, 2011 Math 33A/1 MIDTERM EXAMINATION Spring 2011 Instructions: (a) The exam is closed-book (except for one page of notes) and will last 50 minutes. No calculators, cell phones, or other electronic d
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c solutions From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 addi
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 additional exe
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 2 c c From the textbook solve the problems 17, 18, 19, 22, 23 and 24 from the Chapter 4. Solve the problems 21, 22, 24, 30 from the Chapter 4 additional exercises at http:/www.athenasc.c
School: UCLA
Course: Actuarial Math
Sule Ozler Economics 12 Fall 2011 READ THE EXPLANATIONS IN BOLD LETTERS CAREFULLY! MID-TERM EXAM - GOOD LUCK! WRITE YOUR NAME AND ID# You will not be allowed to ask questions during the exam. This exam has three sections. Each section has multiple questio
School: UCLA
Course: Linear Algebra And Applications
Name: Student ID: Prof. Alan J. Laub Section: 1 April 29, 2011 Math 33A/1 MIDTERM EXAMINATION Spring 2011 Instructions: (a) The exam is closed-book (except for one page of notes) and will last 50 minutes. No calculators, cell phones, or other electronic d
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c solutions From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 addi
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 additional exe
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 2 c c From the textbook solve the problems 17, 18, 19, 22, 23 and 24 from the Chapter 4. Solve the problems 21, 22, 24, 30 from the Chapter 4 additional exercises at http:/www.athenasc.c
School: UCLA
Course: Actuarial Math
Sule Ozler Economics 12 Fall 2011 READ THE EXPLANATIONS IN BOLD LETTERS CAREFULLY! MID-TERM EXAM - GOOD LUCK! WRITE YOUR NAME AND ID# You will not be allowed to ask questions during the exam. This exam has three sections. Each section has multiple questio
School: UCLA
Course: Math 131a
Mathematics 131A - Final Examination Instructor : D. E. Weisbart June 12, 2012 NAME (please print legibly): Your University ID Number: Signature: There are SEVEN questions on this examination. Calculators, notes and books may not be used in this examina
School: UCLA
Course: Linear Algebra
Linear Algebra Math 115AH Midterm 1 Solutions Dominique Abdi 1. If W1 and W2 are subspaces of V and dim(W1 W2 ) = dim W1 what can you say about the relation between W1 and W2 ? Prove your answer. Solution. By the dimension theorem, dim(W1 + W2 ) = dim W1
School: UCLA
Course: Introduction Of Complex Analysis
25 Solution. Consider r1 and r2 such that 0 < R1 < r1 < r2 < R2 . Then f (z) is holomorphic on the (closed) annulus cfw_z : r1 |z| r2 . Thus by Cauchy Integral Theorem, we have f (z) = 1 2i 2 1 f () d z 2i 1 f () d, z where 1 = cfw_z : |z| = r1 and 2
School: UCLA
Course: Probability For Life Sciences Students
Math 3C Exam I Spring 2014 Name _ UCLA ID _ Lecture and Section _ No calculator, no cell phone, no notes. Show all of your work to receive credit . PROBLEM POINTS You earned : 1 5 2 5 3 5 4 5 5 10 6 10 7 10 Total 50 Simplify all answers Part I Counting :
School: UCLA
Course: CALCULUS OF A SINGLE VARIABLE
Math 31A Midterm 1 Solutions 1. [3 points] The derivative of (a) 1 (b) (c) x2 x)2 x3 Brent Nelson is: 1 x2 1 2 x3 (3x 1 1 + x2 + 8x2 x + 3) (d) None of the above. Solution. We rst apply the quotient rule d dx x2 x)2 x3 = d d x3 dx [(x2 x)2 ] (x2 x)2 dx (
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 Due Friday, April 17th From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 Due Friday, April 17th From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 solutions From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:/www.athenasc
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2015 - Homework 7 solutions From the textbook solve the problems 1, 2 and 3 from the Chapter 6. Solve the problems 3, 4, 5, 6, 7, 8 and 9 from the Chapter 5 additional exercises at http:/www.athenasc.com/prob-supp.htm
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 1 Solutions April 7, 2014 Problem 34.4 Suppose the growth rate of a certain species is not constant, but depends in a known way on the temperature of its environment. If the temperature is known as a function of time, derive an expres
School: UCLA
Course: PRECALCULUS PART 1
Math 115 Spring 11 Written Homework 10 Solutions 1. For following limits, state what indeterminate form the limits are in and evaluate the limits. 3x2 4x 4 x2 2x2 8 (a) lim 0 . Algebraically, we hope to be able to factor the 0 numerator and denominator an
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
Math 33B Time table: Lecture time Lecture 2 Lecture 3 Lecture location Midterm 1 Midterm 2 Final time 1111:50am MWF 4000A MS October 31st , Friday. November 24th , Wednesday lecture time, lecture room lecture time, lecture room December 13, 11:30am2:30pm
School: UCLA
Course: MULTIVARIABLE CALCULUS
Mathematica for Rogawski's Calculus 2nd Edition 2010 Based on Mathematica Version 7 Abdul Hassen, Gary Itzkowitz, Hieu D. Nguyen, Jay Schiffman W. H. Freeman and Company New York 2 Mathematica for Rogawski's Calculus 2nd Editiion.nb Copyright 2010 Mathem
School: UCLA
Course: Actuarial Math
172C June 2013 AV, Asset Shares, Year by Year Financial Universal Life Account Values 1. For Universal Life UL policies in particular, the Account Value AV functions like a policy holder "bank account that is periodically updated Even though premium
School: UCLA
Math 172 B Class Project 1 Object: to download a specific mortality table from the Society of Actuaries website and utilize mortality rates to calculate life expectancies Steps: 1. Log onto www.soa.org 2. At the bottom of the opening page, select popular
School: UCLA
Course: Linear Algebra And Applications
Name: Student ID: Prof. Alan J. Laub Section: 1 April 29, 2011 Math 33A/1 MIDTERM EXAMINATION Spring 2011 Instructions: (a) The exam is closed-book (except for one page of notes) and will last 50 minutes. No calculators, cell phones, or other electronic d
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c solutions From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 addi
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 additional exe
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 2 c c From the textbook solve the problems 17, 18, 19, 22, 23 and 24 from the Chapter 4. Solve the problems 21, 22, 24, 30 from the Chapter 4 additional exercises at http:/www.athenasc.c
School: UCLA
Course: Actuarial Math
Sule Ozler Economics 12 Fall 2011 READ THE EXPLANATIONS IN BOLD LETTERS CAREFULLY! MID-TERM EXAM - GOOD LUCK! WRITE YOUR NAME AND ID# You will not be allowed to ask questions during the exam. This exam has three sections. Each section has multiple questio
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Course: ANALYSIS
Math 131a Lecture 2 Spring 2009 Midterm 1 Name: Instructions: There are 4 problems. Make sure you are not missing any pages. Unless stated otherwise (or unless it trivializes the problem), you may use without proof anything proven in the sections of the b
School: UCLA
Course: Math 131a
Mathematics 131A Fall 2007 FINAL Your Name: Signature: INSTRUCTIONS: This is a closed-book test. Do all work on the sheets provided. If you need more space for your solution, use the back of the sheets and leave a pointer for the grader. Good luc
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 Due Friday, April 17th From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 Due Friday, April 17th From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:
School: UCLA
Course: ANALYSIS
Solutions to homework 1 1.5#1 Mis`re version of the take-away game. There are 21 chips, we can remove 1, 2, or 3. e Last player to move loses, hence position 1 is a P-position, from positions 2,3, and 4 we can move to 1, hence these are N-positions. Now,
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 solutions From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:/www.athenasc
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2015 - Homework 7 solutions From the textbook solve the problems 1, 2 and 3 from the Chapter 6. Solve the problems 3, 4, 5, 6, 7, 8 and 9 from the Chapter 5 additional exercises at http:/www.athenasc.com/prob-supp.htm
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 1 Solutions April 7, 2014 Problem 34.4 Suppose the growth rate of a certain species is not constant, but depends in a known way on the temperature of its environment. If the temperature is known as a function of time, derive an expres
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Course: PRECALCULUS PART 1
Math 115 Spring 11 Written Homework 10 Solutions 1. For following limits, state what indeterminate form the limits are in and evaluate the limits. 3x2 4x 4 x2 2x2 8 (a) lim 0 . Algebraically, we hope to be able to factor the 0 numerator and denominator an
School: UCLA
Course: Math 131a
Mathematics 131A - Final Examination Instructor : D. E. Weisbart June 12, 2012 NAME (please print legibly): Your University ID Number: Signature: There are SEVEN questions on this examination. Calculators, notes and books may not be used in this examina
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 6 c c Solve the problems 18 a) c) d) e) and 19 from the Chapter 7 additional exercises at http:/www.athenasc.com/prob-supp.html And also the problems below: Problem 1. Denote points P0 ,
School: UCLA
Course: Casualty Loss Models 2
173B Chapter 6 Review of Hypothesis Testing Panayiotis Skordi 1. Formulate the hypothesis statement for the following claim: The average adult drinks 1.7 cups of coffee per day. A sample of 35 adults drank an average of 1.95
School: UCLA
Course: Probability Theory
Probability Theory, Math 170B, Spring 2013 Note: Although solutions exist on-line, you will be doing yourself a great favor by resorting to them only after you have solved the problem yourself (or at least tried very hard to). From the textbook solve prob
School: UCLA
Course: Optimization
Amanda Nguyen Department of Economics UCLA Economics 103 Introduction to Econometrics Summer 2013 Problem Set 2 - Due Tuesday July 30 From textbook: (all data sets can be found linked to from the class website) 7.10, 7.16 (skip a, e) 10.3 (d, f, g, and h
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 6 Due Friday, May 8th From the books supplementary problems, solve problems 5, 6, 7, 9 and 19 in Chapter 7 (see http:/www.athenasc.com/prob-supp.html). And also the problems below: Pro
School: UCLA
Course: Probability Theory
Probability Theory, Math 170A, Fall 2014 - Homework 5 solutions From the textbook solve the problems 32, 39, 40 at the end of the Chapter 2. Solution to Problem 32: Let Xi be the indicator of the event that the rst person in the i-th couple is alive and Y
School: UCLA
Course: Solution
Solution 4 Sec2.3 2.3.2(a) Let 1 3 1 0 - 3 C = 1 A= -1 2 - 1 , B = 4 1 2 , 1 -2 2 4 , and D = - 2 0 3 Compute A(2B+3C), (AB)D, and A(BD). Ans.: 3 12 5 3 6 2 0 - 6 3 2B+3C= 8 2 4 + - 3 - 6 0 = 5 - 4 4 1 3 5 3 6 20 - 9 18 = A(2B+3C)= 2 - 1 5 - 4 4 5 10 8
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Actuarial Math
Math 172 B Class Project 1 Object: to download mortality tables from the Society of Actuaries website and utilize mortality rates for a selected table to calculate life expectancies Steps: 1. Log onto www.soa.org 2. Put the words Table Manager in the Sear
School: UCLA
Course: Linear Algebra And Applications
Name: Student ID: Prof. Alan J. Laub Section: 1 April 29, 2011 Math 33A/1 MIDTERM EXAMINATION Spring 2011 Instructions: (a) The exam is closed-book (except for one page of notes) and will last 50 minutes. No calculators, cell phones, or other electronic d
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c solutions From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 addi
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 additional exe
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 2 c c From the textbook solve the problems 17, 18, 19, 22, 23 and 24 from the Chapter 4. Solve the problems 21, 22, 24, 30 from the Chapter 4 additional exercises at http:/www.athenasc.c
School: UCLA
Course: Actuarial Math
Sule Ozler Economics 12 Fall 2011 READ THE EXPLANATIONS IN BOLD LETTERS CAREFULLY! MID-TERM EXAM - GOOD LUCK! WRITE YOUR NAME AND ID# You will not be allowed to ask questions during the exam. This exam has three sections. Each section has multiple questio
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Course: ANALYSIS
Math 131a Lecture 2 Spring 2009 Midterm 1 Name: Instructions: There are 4 problems. Make sure you are not missing any pages. Unless stated otherwise (or unless it trivializes the problem), you may use without proof anything proven in the sections of the b
School: UCLA
Course: Math 131a
Mathematics 131A Fall 2007 FINAL Your Name: Signature: INSTRUCTIONS: This is a closed-book test. Do all work on the sheets provided. If you need more space for your solution, use the back of the sheets and leave a pointer for the grader. Good luc
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: ANALYSIS
Solutions to homework 1 1.5#1 Mis`re version of the take-away game. There are 21 chips, we can remove 1, 2, or 3. e Last player to move loses, hence position 1 is a P-position, from positions 2,3, and 4 we can move to 1, hence these are N-positions. Now,
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 6 c c Solve the problems 18 a) c) d) e) and 19 from the Chapter 7 additional exercises at http:/www.athenasc.com/prob-supp.html And also the problems below: Problem 1. Denote points P0 ,
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 6 Due Friday, May 8th From the books supplementary problems, solve problems 5, 6, 7, 9 and 19 in Chapter 7 (see http:/www.athenasc.com/prob-supp.html). And also the problems below: Pro
School: UCLA
Course: Solution
Solution 4 Sec2.3 2.3.2(a) Let 1 3 1 0 - 3 C = 1 A= -1 2 - 1 , B = 4 1 2 , 1 -2 2 4 , and D = - 2 0 3 Compute A(2B+3C), (AB)D, and A(BD). Ans.: 3 12 5 3 6 2 0 - 6 3 2B+3C= 8 2 4 + - 3 - 6 0 = 5 - 4 4 1 3 5 3 6 20 - 9 18 = A(2B+3C)= 2 - 1 5 - 4 4 5 10 8
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Actuarial Math
Math 172 B Class Project 1 Object: to download mortality tables from the Society of Actuaries website and utilize mortality rates for a selected table to calculate life expectancies Steps: 1. Log onto www.soa.org 2. Put the words Table Manager in the Sear
School: UCLA
Course: Linear Algebra And Applications
Name: Student ID: Prof. Alan J. Laub Section: 2 May 4, 2012 Math 33A/2 MIDTERM EXAMINATION Spring 2012 Instructions: (a) The exam is closed-book (except for one page of notes) and will last 50 minutes. No calculators, cell phones, or other electronic devi
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 6 c c Solve the problems 18 a) c) d) e) and 19 from the Chapter 7 additional exercises at http:/www.athenasc.com/prob-supp.html And also the problems below: Problem 1. Denote points P0 ,
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 6 c c Solve the problems 18 a) c) d) e) and 19 from the Chapter 7 additional exercises at http:/www.athenasc.com/prob-supp.html And also the problems below: Problem 1. Denote points P0 ,
School: UCLA
Course: Actuarial Math
Spring 2011- Professor Sule Ozler Name Economics 121 ID# FINAL EXAM WRITE YOUR NAME AND ID# No questions will be answered during the exam There will not be any bathroom breaks during the exam You are permitted to have only your writing equipment on your d
School: UCLA
Course: MULTIVARIABLE CALCULUS
572 C H A P T E R 14 C A L C U L U S O F VE C T O R - VA L U E D F U N C T I O N S SOLUTION (ET CHAPTER 13) Keplers Third Law states that the period T of the orbit is given by: T2 = 4 2 GM a3 or 2 3/2 T= a GM If a is increased four-fold the period becomes
School: UCLA
Course: MATH20F
Hector Ordorica Section: B51 / B02 TA: Matthew Cecil Exercise 3.1 Answer: D can be: 1. D = 0 0 00 2. D = 1 0 01 3. D = 0 1 10 Exercise 3.2 (a) Input: A = [1, 2, 0; 2, 1, 2; 0, 2, 1] B = [3, 0, 3; 1, 5, 1; 1, 1, 3] x = [1; 2; 3] C = (5*A^2*B - 3*A')^2 Outp
School: UCLA
Course: Probability Theory
T. Liggett Mathematics 170B Midterm 2 Solutions May 23, 2012 (20) 1. (a) State Markovs inequality. Solution: If X 0, then P (X a) EX/a for a > 0. (b) Prove Markovs inequality. Solution: a1cfw_X a X . Taking expected values gives aP (X a) EX . (c) Suppose
School: UCLA
Course: Actuarial Math
Math 172A Exam 1 10/22/10 Name: _ 1. Deposit to fund: $3,000 paid on 1/1/2010 Withdrawal from fund: $1,000 on 1/1/2015 Interest accumulates at the following rates for the various periods specified: 2010 through 2012: 2013 through 2016: 2017 through 2022:
School: UCLA
Course: Linear Algebra
Answer Key to Second Midterm Examination, Version 1 1. Answer the following questions: (1) Let T : V V be a linear transformation of a nite dimensional vector space V . Prove that T : V V is not invertible if rank(T 2) < dim V . (20 points) If T is invert
School: UCLA
Course: Linear Algebra
Sample Final Examination Print your name: (last) (rst) Student ID number: (middle initial) - Sign in full name: 1. /120 2. /120 3. /150 4. /110 Total /500 Note: (1) Keep your desktop clean. Put your textbooks and notebooks in your bag and keep them closed
School: UCLA
Course: Math 131a
Mathematics 131A - Final Examination Instructor : D. E. Weisbart June 12, 2012 NAME (please print legibly): Your University ID Number: Signature: There are SEVEN questions on this examination. Calculators, notes and books may not be used in this examina
School: UCLA
Course: Linear Algebra
Linear Algebra Math 115AH Midterm 1 Solutions Dominique Abdi 1. If W1 and W2 are subspaces of V and dim(W1 W2 ) = dim W1 what can you say about the relation between W1 and W2 ? Prove your answer. Solution. By the dimension theorem, dim(W1 + W2 ) = dim W1
School: UCLA
Course: Introduction Of Complex Analysis
25 Solution. Consider r1 and r2 such that 0 < R1 < r1 < r2 < R2 . Then f (z) is holomorphic on the (closed) annulus cfw_z : r1 |z| r2 . Thus by Cauchy Integral Theorem, we have f (z) = 1 2i 2 1 f () d z 2i 1 f () d, z where 1 = cfw_z : |z| = r1 and 2
School: UCLA
Course: Probability For Life Sciences Students
Math 3C Exam I Spring 2014 Name _ UCLA ID _ Lecture and Section _ No calculator, no cell phone, no notes. Show all of your work to receive credit . PROBLEM POINTS You earned : 1 5 2 5 3 5 4 5 5 10 6 10 7 10 Total 50 Simplify all answers Part I Counting :
School: UCLA
Course: CALCULUS OF A SINGLE VARIABLE
Math 31A Midterm 1 Solutions 1. [3 points] The derivative of (a) 1 (b) (c) x2 x)2 x3 Brent Nelson is: 1 x2 1 2 x3 (3x 1 1 + x2 + 8x2 x + 3) (d) None of the above. Solution. We rst apply the quotient rule d dx x2 x)2 x3 = d d x3 dx [(x2 x)2 ] (x2 x)2 dx (
School: UCLA
Course: Math32A
Management 1A Winter 2004 Danny S. Litt Exam 3 Solutions Name: _ PROBLEM POINTS SCORE 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 TOTAL 100 Management 1A Problem 1 Winter 2004 (a) A company purchased a patent on January 1, 2002, for $1,000,
School: UCLA
Course: Math32A
MATH 32A FINAL EXAMINATION March 21th, 2012 Please show your work. You will receive little or no credit for a correct answer to a problem which is not accompanied by sucient explanations. If you have a question about any particular problem, please raise y
School: UCLA
Course: Probability Theory
INTRODUCTION TO PROBABILITY by Dimitri P. Bertsekas and John N. Tsitsiklis CHAPTER 2: ADDITIONAL PROBLEMS SECTION 2.2. Probability Mass Functions Problem 1. The probability of a royal ush in poker is p = 1/649, 740. Show that approximately 649, 740 hands
School: UCLA
Course: Linear Algebra And Applications
1.1 Introduction to Linear Systems 5 A System without Solutions In the following system, perform the eliminations yourself to obtain the result shown: x 4x 7x + 2y + 3;: = + 5y + 6z = + 8y + 9z = x 0 3 - y -+ z= 2 + 2z =-1 0= -6 0 Whatever values we choos
School: UCLA
Course: Linear Algebra And Applications
Math 33A Final Study Guide Instructor: David Wihr Taylor Fall Quarter, 2014 1 Overview The nal exam is cumulative and will cover all the material in the lectures. Your review should, therefore, include the information on the study guide for the rst midter
School: UCLA
Course: Linear Algebra And Applications
Math 33A Exam #1 Study Guide Instructor: David Wihr Taylor Fall Quarter 2014 1 Overview The rst midterm exam will cover all the material in the lectures, which corresponds to the material in sections 1.1-2.4 of the text book. Below is a list of denitions,
School: UCLA
MATH 33B MIDTERM 1 Name: section: ID: 1. (35 points) Find the general solution to the dierential equation (a) = . (b) = + (c) = 4 sin (d) = + . (Hint: let = 2 ) Solve the initial value problem: (e) + = 0 with (1) = 2. 1 2. (20 points)Find a general solu
School: UCLA
Course: Linear Algebra
Name: Math 115A Spring 2013 Final Practice There are three sections of questions. The rst section contains problems that are relatively straightforward. The second section is problems on the adjoint of a linear operator and selfadjoint (or symmetric) line
School: UCLA
Course: Linear Algebra
Name: Math 115A May 24, 2013 Exam 2 Practice SID: (1) Let V be a 4 dimensional vector space with basis = (x1 , x2 , x3 , x4 ). Let T : V V be the linear operator with T (x1 ) = 2x1 T (x2 ) = 0 T (x3 ) = 2x1 T (x4 ) = 3x2 + 3x4 . Find [T ] . (2) In 33A we
School: UCLA
Course: Linear Algebra
Name: Math 115A May 24, 2013 Exam 2 SID: There are 4 questions worth a total of 20 points. You may use any result from class or the book. Write clearly and in complete sentences (except for the true/false questions). Please ask if you have any questions.
School: UCLA
Course: Math
1 1. Find all the local minimizers of the function f (x) = f (x1 , x2 ) = x3 + x3 3x1 x2 + 3. 1 2 2. Use Newtons method to nd a stationary point of 3 f (x) = f (x1 , x2 ) = 2 x2 + x1 x2 + x2 x1 + 2x2 + 5 1 2 starting with x0 = (3, 1)T . 3. Consider the pr
School: UCLA
Course: Math
1. Exprﬁ (2, 2)T as a, convex combination of (0,1)T,(1,4)T and (3,1)T. 2471+ é[;]-+c[f] 32: Lﬁ’gC big’gc' 0’2 :(l‘i‘l’fo'i'C ' L )« adrlwrc )HOHQ” QECLMIIC'fY a »- (3+3 (L J L3: - g .N 3 2. In solving a linear programming problem by the simplex method, w
School: UCLA
Course: Math
.1. Find all the lotal minimizers of the func’ﬁion 3%} =§iﬁzs£€§z3 =$§%$§"3$1%+3L _ ‘ . . a : szﬂwgﬁa] [U] x, V; Vii/£11595): 0 P” w ' if} g 7, K V3P(010)2ZV: HEN) 3 {\JIA”(7:0 {\zig [JV VquL/Zaﬁ 2. Use Newton’s method to ﬁnd a stationary point of f($);f(
School: UCLA
Course: MULTIVARIABLE CALCULUS
MATHBZA / 2, R. KOZHAN MIDTERMZ MAR 04, 2013 CIRCLE YOUR TA AND DISCUSSION SESSION: 2A—TUES—STEPHAN1E L. 2C—TUEs—IOANNIS L. 2E—TUES—ZACH N. 2B—THUR—STEPHANIE L. 2D—THUR—IOANNIS L. 2F—THUR—ZACH N. Instructions: 0 If you get stuck, move on to the next quest
School: UCLA
Name » g3] “mags ll 7. Math 1728—1 Quiz 3 To become a graduate at "Prestigious University”, each incoming freshman must pass 4 years’ worth of classes. Out of 5,000 incoming freshman (the radix), only 480 graduate. You are also given the following: 1|qo =
School: UCLA
Management 122 1,: Spring 22.015 Danny S. Litt EXAM 1 I agree to have my grade poste‘i b Student ID Number _— I .M m“. ~ . r - ,A _ . . ma. Q. J ‘ 1, 1'; ~‘ ’ A. . ‘ i. 4 (Signature) Name: PI n , W _ . NM \ For each ofthe following, choose the
School: UCLA
CalCU1I1tep(X), the fon:e ofmOJ1!llitY. I S C IC) ., c. )~ D. 5l:7In(3Sx~ E. 35;<',-4>' l-e ! .' c . - CONTJNUED ON NEXTPAG;E 15 ( -S2:-1 ~ ham 3, S]l<ios lom 6. , You are given !hesurvival fUDction S(.%) =1 - .%. 10,000 'for x<:IOO. . Calcula!e A. B. C.
School: UCLA
SOL—How) Name Math 1728-1 Quiz 2 Joe has children who use legos to destroyJoe’s precious musical instruments. Today, Joe threw his old guitar in the trash and bought a new one. Because the kids are getting bigger, stronger, and more destructive, Joe belie
School: UCLA
Math 172B-1: Quiz 1 1. Melissa decides to buy a used car worth $10,000 at the car dealership today. She took Math 172A at the best university in the world (objectively speaking) last quarter, so she feels sufficiently confident with her background in inte
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 Due Friday, April 17th From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 Due Friday, April 17th From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 solutions From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:/www.athenasc
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2015 - Homework 7 solutions From the textbook solve the problems 1, 2 and 3 from the Chapter 6. Solve the problems 3, 4, 5, 6, 7, 8 and 9 from the Chapter 5 additional exercises at http:/www.athenasc.com/prob-supp.htm
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 1 Solutions April 7, 2014 Problem 34.4 Suppose the growth rate of a certain species is not constant, but depends in a known way on the temperature of its environment. If the temperature is known as a function of time, derive an expres
School: UCLA
Course: PRECALCULUS PART 1
Math 115 Spring 11 Written Homework 10 Solutions 1. For following limits, state what indeterminate form the limits are in and evaluate the limits. 3x2 4x 4 x2 2x2 8 (a) lim 0 . Algebraically, we hope to be able to factor the 0 numerator and denominator an
School: UCLA
Course: Casualty Loss Models 2
173B Chapter 6 Review of Hypothesis Testing Panayiotis Skordi 1. Formulate the hypothesis statement for the following claim: The average adult drinks 1.7 cups of coffee per day. A sample of 35 adults drank an average of 1.95
School: UCLA
Course: Probability Theory
Probability Theory, Math 170B, Spring 2013 Note: Although solutions exist on-line, you will be doing yourself a great favor by resorting to them only after you have solved the problem yourself (or at least tried very hard to). From the textbook solve prob
School: UCLA
Course: Optimization
Amanda Nguyen Department of Economics UCLA Economics 103 Introduction to Econometrics Summer 2013 Problem Set 2 - Due Tuesday July 30 From textbook: (all data sets can be found linked to from the class website) 7.10, 7.16 (skip a, e) 10.3 (d, f, g, and h
School: UCLA
Course: Probability Theory
Probability Theory, Math 170A, Fall 2014 - Homework 5 solutions From the textbook solve the problems 32, 39, 40 at the end of the Chapter 2. Solution to Problem 32: Let Xi be the indicator of the event that the rst person in the i-th couple is alive and Y
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a, Fall 2014- Homework 3 solution From the textbook solve the problems 30, 33, 34, 35 and 36 at the end of the Chapter 1. Solution to Problem 30: In the rst case the hunter could choose the correct path either if both dogs choo
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b - Homework 5 From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com/prob-supp.html And also the pro
School: UCLA
Course: FOUNDATIONS OF TIGHT CLOSURE THRY
Classical Mechanics - Homework Assignment 9 Alejandro Gmez Espinosa o November 29, 2012 Goldstein, Ch.9, 11 Determine whether the transformation is canonical Q1 = q1 q2 Q2 = q1 + q2 p1 p2 +1 q2 q1 q2 p2 q1 p1 P2 = + (q2 + q1 ) q2 q1 P1 = To determine if t
School: UCLA
Course: Introduction Of Complex Analysis
132 Homework 1 solutions Exercise 1 Suppose |z| = 1 and |a| < 1. Show that, za =1 1 az Solution. First, we must show that the left hand side is even dened, i.e. we are not dividing by zero. To show that 1 az = 0 is the same as to show that 1 = az. As |az|
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 3 Solutions May 2, 2014 Problem 44.3 Consider the following nonlinear systems: dy dx = ex 1 = yex (i) dt dt dx dy (ii) = x2 + y 2 1 =x+y dt dt dy dx = x2 + y 2 5 = x2 + 2y 2 9 (iii) dt dt dx dy (iv) = x2 + y 2 1 =x4 dt dt (a) Determin
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 6, solutions Due Friday, May 8th From the books supplementary problems, solve problems 5, 6, 7, 9 and 19 in Chapter 7 (see http:/www.athenasc.com/prob-supp.html). And also the problems
School: UCLA
Course: Math 170
Probability Theory, Math 170A - Homework 4 From the textbook solve the problems 16, 22, 24 at the end of the Chapter 2. Solve the problems 5 and 13 from the Chapter 2 additional exercises at http:/www.athenasc.com/prob-supp.html Problem 1. Recall Problem
School: UCLA
Course: Multivariable Calculus
S E C T I O N 17.1 Vector Fields (ET Section 16.1) 1061 19. F = x, 0, z SOLUTION This vector field is shown in (A) (by process of elimination). x x 2 + y2 + z2 , y x 2 + y2 + z2 , z x 2 + y2 + z2 20. F = SOLUTION The unit radial vector field i
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 5 Due Friday, May 1st From the books supplementary problems, solve problems 21, 22, 27 and 28 in Chapter 4, as well as 1, 3 and 4 in Chapter 7 (see http:/www.athenasc.com/probsupp.html
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a, Winter 2014, Homework 6 From the textbook solve the problems 32, 39, 40 at the end of the Chapter 2. And also the problems below (several of these problems refer to previous homework exercises you can read and make use of th
School: UCLA
Course: Math32A
Math 32A Sections 2 & 4 Fall 2013 Problem Set # 3 (W Problem (1) A line in the plane is given in the (old fashioned) form y = mx+b. Find the shortest distance from the origin to this line. 4 '3 r haul) {l rm) . (Vii-\i) To l (16; x «Rh-u) :0 r g'
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a - Homework 1 solutions Problem 1. Show that for any sets A and B P(A B) P(A) P(A B). Solution: One way to solve it is to notice that A B A and A A B and use the properties of the probability law (in particular the monotonicit
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 0 Solution 32.11 The easier way: (slightly unrigorous, but its ne for this class) Suppose the bank compounds the interest n times a year, and let t := 1/n. With the additional deposit (or withdrawl) D (t), the balance at time t + t is gi
School: UCLA
Course: Math32A
780 C H A P T E R 15 D I F F E R E N T I AT I O N I N S E V E R A L VA R I A B L E S (ET CHAPTER 14) 20. Show that the point (x 0 , y0 ) closest to the origin on the line ax + by = c has coordinates ac bc , y0 = 2 x0 = 2 a + b2 a + b2 SOLUTION We
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b - Homework 4 Problem 1. Show that for random variables X, Y and Z we have E[E[E[X|Y ]|Z] = E[X]. Apply this formula to the following problem: Roll a far 6-sided die and observe the number Z that came up. Then toss a fair coin
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 1 Solution 34.5 (a) If the growth rate is 0, the discrete model becomes Nm+1 Nm = tfm , And the solution is Nm = N0 + t(f0 + f1 + fm1 ), which is analogous to integration, since let t = mt, then t t(f0 + f1 + fm1 ) f (s)ds 0 for t small
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 2 Solution 34.16 We will rstly proceed similarly as 34.14(c). We assume the theoretical growth has the form N0 eR0 t , and we hope to gure out which N0 and R0 t the data best. 34.14(b) suggests that N0 should be equal to the initial popu
School: UCLA
Course: Math 170
Probability Theory, Math 170a, Winter 2015 - Homework 1 From the textbook solve the problems 2, 5-10 at the end of the Chapter 1. And also the problems below: Problem 1. Show that for any sets A and B P(A B) P(A) P(A B). Problem 2. We have a very weird di
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 1 Solution 32.3 (a) Use N (nt) to denote the population at time nt. Then for any n > 0, we have N (nt) = (1 + (b d)t)N (n 1)t) + 1000. (b) Given that N (0) = N0 , we hope to solve the equation above and get the general form for N (nt). T
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
Math 33B Time table: Lecture time Lecture 2 Lecture 3 Lecture location Midterm 1 Midterm 2 Final time 1111:50am MWF 4000A MS October 31st , Friday. November 24th , Wednesday lecture time, lecture room lecture time, lecture room December 13, 11:30am2:30pm
School: UCLA
Course: MULTIVARIABLE CALCULUS
Mathematica for Rogawski's Calculus 2nd Edition 2010 Based on Mathematica Version 7 Abdul Hassen, Gary Itzkowitz, Hieu D. Nguyen, Jay Schiffman W. H. Freeman and Company New York 2 Mathematica for Rogawski's Calculus 2nd Editiion.nb Copyright 2010 Mathem
School: UCLA
Course: Actuarial Math
172C June 2013 AV, Asset Shares, Year by Year Financial Universal Life Account Values 1. For Universal Life UL policies in particular, the Account Value AV functions like a policy holder "bank account that is periodically updated Even though premium
School: UCLA
Math 172 B Class Project 1 Object: to download a specific mortality table from the Society of Actuaries website and utilize mortality rates to calculate life expectancies Steps: 1. Log onto www.soa.org 2. At the bottom of the opening page, select popular