Math 170B - Probability Theory, Lec.1, Spring 2016 - Homework 6
Due: Tuesday, November 8th 2016, at the beginning of class.
From the textbook, solve problems 5, 8, 10 and 11 at the end of Chapter 5.
F
Math 170B - Probability Theory, Lec.1, Fall 2016 - Homework 5
Due: Tuesday, November 1st 2016, at the beginning of discussion.
From the textbook, solve problems 4 and 5 at the end of Chapter 5. Moreov
Math 170B - Probability Theory, Lec.1, Fall 2016 - Homework 7
Due: Tuesday, November 15th 2016, at the beginning of discussion.
From the books supplementary problems, solve problems 18 (a), (c), (d),
Math 170B - Probability Theory, Lec.1, Fall 2016 - Homework 9
Due: Tuesday, November 29th 2016, at the beginning of discussion.
From the textbook, solve problems 8, 9, 10, 11, 12, 13 and 16 at the end
Math 170B - Probability Theory, Lec.1, Fall 2016 - Homework 8
Due: Tuesday, November 22nd 2016, at the beginning of discussion.
From the textbook, solve problems 1, 2 and 3 at the end of Chapter 6.
Fr
Math 170B - Probability Theory, Lec.1, Fall 2016 - Homework 4
Due: Tuesday, October 25th 2016, at the beginning of discussion.
From the textbook, solve problems 29, 30, 31, 32, 33 at the end of Chapte
Math 170B
Midterm 2
November 20
Answer the questions in the spaces provided on the question sheets. If you
run out of room for an answer, continue on the back of the page. Explain
your answers and rea
Midterm 1, Math 170B - Winter 2016
Printed name:
Signed name:
Student ID number:
(By signing here, I certify that I have taken this test while refraining from cheating.)
Instructions:
If you are foun
Useful formulas.
o PMF 0f Bernouli (p): pX(1) = p,pX(0) = p.
Expectation is p, variance is p(1 p).
o PMF 0f Bin(n,p):
Expectation is np. Variance is np(1 p).
o PMF of Geo(p):
1 1
Expectation is . Vari
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_Xa X. Ta
Math 170B - Probability Theory, Lec.1, Fall 2015 - Homework 5
Due: Wednesday, Oct. 28th 2015, at the beginning of class.
From the textbook, solve problems 4 and 5 at the end of Chapter 5. Moreover,
wo
Convergence of random variables
In this note, we explain the three different definitions of convergence of
random variables.
Let X1 , X2 , be a sequence of random variables which come from the
same ex
Probability Theory, Math 170B, Winter 2016 - Homework 1
Extra problems:
Problem 1. Suppose that X1 and X2 are two independent exponential
random variables with parameters 1 and 2 respectively.
(a) Wha
Math 170B - Probability Theory, Lec.1, Fall 2015 - Homework 7
Due: Friday(!), Nov. 13th 2015, at the beginning of class.
From the books supplementary problems, solve problems 18 (a), (c), (d), (e) and
Identical distribution
In this note, we explain the concept of identical distribution.
Given two random variables X and Y (not necessary come from the same
experiment), that is,
X : 1 R
and
Y : 2 R,
w
Math 170B - Probability Theory, Lec.1, Fall 2015 - Homework 4
Due: Wednesday, Oct. 21st 2015, at the beginning of class.
From the textbook, solve problems 29, 30, 31, 32, 33 at the end of Chapter 4.
M
Useful formulas.
E[X|Y ] is the random variable which is equal to E[X|Y = k] when Y = k.
var(X|Y ) is the random variable which is equal to var[X|Y = k] when Y = k. Alternate
formula,
var(X|Y ) = E(X
Math 170B - Probability Theory, Lec.1, Fall 2015 - Homework 8
Due: Friday, Nov. 20th 2015, at the beginning of class.
From the textbook, solve problems 1, 2 and 3 at the end of Chapter 6.
From the boo
Probability Theory, Math 170B, Winter 2016 - Homework 5
Extra problems:
Problem 1. (a) Show that if
| maxcfw_0, a maxcfw_0, b| > 0
then
|a b| .
(b) Show that if Xn X in probability then maxcfw_0, Xn
Math 170B - Probability Theory, Lec.1, Fall 2015 - Homework 2
Due: Wednesday, Oct. 7th 2015, at the beginning of class.
From the books supplementary problems, solve problems 15, 16, 17, 30, 31, 32
in
Math 170B Probability Theory: Lecture 13
Yuan Zhang
[email protected]
Department of Mathematics
UCLA
April 29th 2016
Yuan Zhang (Dept. Math, UCLA)
Probability Theory
April 29th 2016
1 / 11
Conve
Math 170B Probability Theory: Lecture 20
Yuan Zhang
[email protected]
Department of Mathematics
UCLA
May 27th 2016
Yuan Zhang (Dept. Math, UCLA)
Probability Theory
May 27th 2016
1/8
Final Exam
T
Math 170B Probability Theory: Lecture 11
Yuan Zhang
[email protected]
Department of Mathematics
UCLA
April 25th 2016
Yuan Zhang (Dept. Math, UCLA)
Probability Theory
April 25th 2016
1 / 11
Limit
Math 170B Probability Theory: Lecture 12
Yuan Zhang
[email protected]
Department of Mathematics
UCLA
April 27th 2016
Yuan Zhang (Dept. Math, UCLA)
Probability Theory
April 27th 2016
1/9
Weak Law
Math 170B Probability Theory: Lecture 7
Yuan Zhang
[email protected]
Department of Mathematics
UCLA
April 11th 2016
Yuan Zhang (Dept. Math, UCLA)
Probability Theory
April 11th 2016
1/9
Condition