We aren't endorsed by this school 
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

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

homework3
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:

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

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

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

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

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

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 ,

homework6solutions
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 ,

solution_4
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

midterm_2
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

homework6
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 ,

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

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

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_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

math170bhw1
School: UCLA
Course: Probability
Mathematics 170B HW1 Due Thursday, January 6, 2011. Problems 1, 2, 3, 4 on page 246. (Note: On problem 4, the PDF of X is general not the uniform from Example 3.14 in Chapter 3.) The following problems are from my 170A nal exam last Fall. They are the one

homework2
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

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

hwk3
School: UCLA
Course: Probability
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
Course: Probability
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
Course: Probability
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
Course: Probability
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
Course: Probability
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
Course: Probability
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
Course: Probability
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

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