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MATH 170b  Probability Theory  UCLA Study Resources

homework3
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

homework1solutions
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

homework4solutions
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

midterm_1_practice_2solutions
School: UCLA
Course: Probability Theory
Midterm 1 practice, Math 170b  Lec 1, Winter 2013 Instructor: Toni Antunovi c c Name and student ID: Question Points 1 10 2 10 3 10 4 10 5 10 Total: 50 Score 1. (a) (2 points) If is a sample space, what is P(). Solution: P() = 1 (b) (2 points) If P(A) =

midterm_2solutions
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

midterm_3solutions
School: UCLA
Course: Probability Theory
Midterm 3, 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

math 170b sol
School: UCLA
Introduction to Probability 2nd Edition Problem Solutions (last updated: 11/25/11) c Dimitri P. Bertsekas and John N. Tsitsiklis Massachusetts Institute of Technology WWW site for book information and orders http:/www.athenasc.com Athena Scientific, Belmo

homework3solutions
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

homework6solutions winter
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/probsupp.html And also the problems below: Problem 1. Denote points P0 ,

homework5
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi  Homework 5 c c From the textbook solve the problems 4 and 5 from the Chapter 5. Solve the problems 2, 4, 6, 7, 9 and 10 from the Chapter 7 additional exercises at http:/www.athenasc.com/probsupp

homework2solutions
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

homework4
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

PracticeFinal_SolsSec1
School: UCLA

SolutionsHwk1
School: UCLA

midterm_2_practice_1solutions
School: UCLA
Course: Probability Theory
Midterm 2 practice, Math 170b, Spring 2015 Name and student ID: Question Points 1 10 2 10 3 10 4 10 Total: 40 Score 1. (a) (2 points) Can a random variable have the same PDF and CDF? Justify your reasoning. Solution: No. The CDF FX is always nonnegative

Midterm #2 Solutions
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

PracticeFinal
School: UCLA
UCLA id: Name: Math 170b Winter 2012 Final Exam Section Points Grade I 35 II 32 III 33 Total 100 This is a practice nal. For the sake of time, I did not add more problems than can be solved. Expect the real nal to require solving the same amount of probl

Midterm #1 Solutions
School: UCLA
Course: Probability Theory
T. Liggett Mathematics 170B Midterm 1 Solutions April 25, 2012 (10) 1. Suppose X has the Cauchy density 1 , < x < . f (x) = (1 + x2 ) Find the density of Y = 2X + 1. Solution: y 1 2 y1 1 = dx, P (Y y ) = P X 2 2 (1 + x ) so Y has density 2 1 . 4 + (y

Homework Solutions
School: UCLA
Course: Probability Theory
Mathematics 170B Selected HW Solutions. F4 . Suppose Xn is B (n, p). (a) Find the moment generating function Mn (s) of (Xn np)/ np(1 p). Write q = 1 p. The MGF of Xn is (pes + q )n , since Xn can be written as the sum of n independent Bernoullis with para

hwk1
School: UCLA
Math 170B Winter 2014 Homework 1 Suggested reading: Sections 4.1, 4.2, and 4.3. Read the solutions to Problem 15, Problem 20 from the end of Chapter 4. Problems: (1) Solve problems 5, 18 and 19 from Chapter 3. (2) Solve problems 5, 7 and 14 from Chapter

hwk3
School: UCLA
Math 170B Winter 2014 Homework 3 Suggested reading: Section 5.1. Read the solutions to Problems 39, 45 from the end of Chapter 4. Problems: (1) Solve Problems 34, 35, 42 and 43 from Chapter 4. (2) Compute (a) X is (b) X is (c) X is (d) X is (e) X is a f

hwk2
School: UCLA
Math 170B Winter 2014 Homework 2 Suggested reading: Section 4.4. Read the solutions to Problems 21, 25, 26 and 27 from the end of Chapter 4. Problems: (1) Solve Problems 10, 11, 12, 29, 32 and 33 from Chapter 4. (2) A fair die is tossed n times, let X d

hwk4
School: UCLA
Math 170B Winter 2014 Homework 4 Suggested reading: Sections 5.2, 5.3 and 5.4. Read the solutions to Problem 2 (Cherno bound) from the end of Chapter 4. Problems: (1) Solve Problems 1, 4 and 5 from Chapter 5. (2) Let X1 , X2 , X3 , . . . be a sequence o

hwk5
School: UCLA
Math 170B Winter 2014 Homework 5 Suggested reading: Section 5.5. Solutions to problems 12, 18 at the end of chapter 5. Notes (posted on my homepage/CCLE) about the BerryEssen Theorem. Problems: (1) Let X1 , X2 , . . . be i.i.d and uniformly distribute

hwk6
School: UCLA
Math 170B Winter 2014 Homework 6 Suggested reading: Section 6.1 (note: it is a longer section than usual). Keep in mind that I will be departing at times from the book, adding some extra material during lectures. Notably, the Gamblers ruin example from

hwk7
School: UCLA
Math 170B Winter 2014 Homework 7 Suggested reading: Section 6.2. Solutions to Problems 4, 19, 22. Problems: (1) Solve problems 12, 13 and 16 at the end of chapter 6. (2) We are given a biased coin for which the probability of heads is p (0 < p < 1). (a)

hwk3
School: UCLA
Math 170B Winter 2014 Homework 3 Suggested reading: Section 5.1. Read the solutions to Problems 39, 45 from the end of Chapter 4. Problems: (1) Solve Problems 34, 35, 42 and 43 from Chapter 4. (2) Compute (a) X is (b) X is (c) X is (d) X is (e) X is a f

BerryEsseen
School: UCLA
The BerryEsseen inequality Let X1 , X2 , . . . be an innite i.i.d. sequence of random variables. If and common mean and variance, dene Sn by p n X1 + . . . + Xn Sn = . n 2 denote their Then, the BerryEsseen inequality is (x) p FSn (x) n 3 , (BE) whe

SolutionsHwk2
School: UCLA

SolutionsHwk3
School: UCLA