Midterm 2, Math 170B — Lec. 1, Fall 2015
Instructor: Pierre-Frangois Rodriguez
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Printed name:
Signed name:
Student ID number:
Instructions:
0 Read the following problems very carefully.
o The correct ﬁnal answer alone is not sufﬁcient for fu
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c
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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
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
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
Math 170B Practice Exam 1
1. (15 points) Let X, Y be two random variables, with var(X) = 1, var(Y ) = 4, cov(X, Y ) = 1.
Find var(X + 2Y ).
2. (20 points) Suppose X has the Cauchy density
fX (x) =
1
, x R.
(1 + x2 )
Find the probability density function o
Midterm 1, Math 170B v Lee. 1, Fall 2015
Instructor: Pierre—Francois Rodriguez
Printed name:
Signed name:
Student 'ID number:
Instructions:
0 Read the following problems very carefully.
o The correct ﬁnal answer alone is not sufﬁcient for full credi
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:
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
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
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
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
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 ,
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
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
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
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
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 ,
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
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 ,
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) =
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
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
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
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/prob-supp
170B Homework 2- Due Friday, October 9nd.
Homework should be written neatly and clearly explained. If it requires more than one
sheet, the sheets must be stapled. Include your name and id number in the top right corner
of your homework.
From the textbook
Math 170B Probability Theory: Lecture 10
Yuan Zhang
yuanzhang@math.ucla.edu
Department of Mathematics
UCLA
February 1st 2016
Yuan Zhang (Dept. Math, UCLA)
Probability Theory
February 1st 2016
1/6
Summation of Random Number of Random Variables
In previous
Math 170B Probability Theory: Lecture 1
Yuan Zhang
yuanzhang@math.ucla.edu
Department of Mathematics
UCLA
January 4th 2016
Yuan Zhang (Dept. Math, UCLA)
Probability Theory
January 4th 2016
1/9
Course Information
Course Title: Probability Theory (Part 2)
T
Math 170B Probability Theory: Lecture 11
Yuan Zhang
yuanzhang@math.ucla.edu
Department of Mathematics
UCLA
February 5th 2016
Yuan Zhang (Dept. Math, UCLA)
Probability Theory
February 5th 2016
1 / 11
Limit Theorems
In this chapter we will learn two very im
Math 170B Probability Theory: Lecture 13
Yuan Zhang
yuanzhang@math.ucla.edu
Department of Mathematics
UCLA
February 12th 2016
Yuan Zhang (Dept. Math, UCLA)
Probability Theory
February 12th 2016
1/6
The Central Limit Theorem
In the weak law of large number
Math 170B - Probability Theory, Lec.1, Fall 2016 - Homework 2
Due: Tuesday, October 11th 2016, at the beginning of discussion.
From the books supplementary problems, solve problems 15, 16, 17, 30, 31, 32
in Chapter 4 (see http:/www.athenasc.com/prob-supp.
Math 170B - Probability Theory, Lec.1, Fall 2016 - Homework 3
Due: Tuesday, October 18th 2016, at the beginning of discussion.
From the textbook, solve problems 22 and 23 at the end of Chapter 4.
From the books supplementary problems, solve problems 21, 2
Math 170B - Probability Theory, Lec.1, Fall 2016 - Homework 1
Due: Tuesday, October 4th 2016, at the beginning of discussion.
From the textbook Introduction to probability, 2nd Ed., by D. P. Bertsekas and
J. N Tsitsiklis, solve the problems 1, 2, 3, 5, 6
170B Probability Theory
Puck Rombach
Homework 1, due: 9/30/16.
Problem 1
Suppose that X and Y are independent, identically distributed, geometric random variables with
parameter p. Show that
P(X = i|X > Y) > 2P(X = i)P(Y < i).
.
Problem 2
You have lost yo