Mathematics Department, UCLA T. Richthammer
spring 09, sheet 1 Mar 30, 2009
Homework assignments: Math 170B Probability, Sec. 1
01. Let X be a normal RV with parameters , 2 , and a, b R. (a) Show that Y = aX + b again is a normal RV (with which parameters

Mathematics Department, UCLA T. Richthammer
spring 09, sheet 3 Apr 10, 2009
Homework assignments: Math 170B Probability, Sec. 1
19. Calculate the expectation and the variance for the sum of 12 rolls of a fair die. Answer: X = X1 + . . . + X12 , where the

Mathematics Department, UCLA T. Richthammer
spring 09, sheet 2 Apr 03, 2009
Homework assignments: Math 170B Probability, Sec. 1
10. X, Y have the joint PDF f (x, y ) = xex(y+1) 1cfw_x,y>0 . Calculate (a) E
eXY (1+Y )2
(b) E(X )
(c) E(XY )
(d*) E(Y )
Would

Mathematics Department, UCLA T. Richthammer
spring 09, sheet 4 Apr 17, 2009
Homework assignments: Math 170B Probability, Sec. 1
33. Let X1 , . . . , Xn a Bernoulli sequence with success rate p (i.e. the Xi are independent, have values 0 or 1 and P (Xi = 1

Mathematics Department, UCLA T. Richthammer
spring 09, sheet 7 May 8, 2009
Homework assignments: Math 170B Probability, Sec. 1
(1 65. Here we will show that E( X1 ) = 1(np)p for a binomial RV X with parameters n, p: +1 +1) Let X1 , . . . , Xn+1 be a Berno

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 Theorems
In this chapter we will learn two very import

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
Time: Wednesday June 8th, 2016, 11:30 AM - 2:30 PM
Locat

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
Convergence in Probability
Here we will have another example

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 of Large Numbers
In the previous lecture, we used Mark

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 Chapter 4.
Moreover, solve the problems below:
Problem 1. Giv

Mathematics Department, UCLA T. Richthammer
spring 09, sheet 5 Apr 24, 2009
Homework assignments: Math 170B Probability, Sec. 1
42. Choose a number n completely at random from cfw_1, 2, 3, 4, then choose a number k completely at random from cfw_1, . . . ,

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.
From the books supplementary problems, solve problems 3,

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 of
Chapter 6.
From the books supplementary problems, s

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), (e) and
19 in Chapter 7 (see http:/www.athenasc.com/pro

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. Moreover,
work through problem 2 (Chernov bound) which is sol

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
Conditional Expectation
Finally, we have the following property

Midterm 1, Math 170b - Lec 1, Spring 2013
Instructor: Toni Antunovi
c
c
Printed name:
Signed name:
Student ID number:
Instructions:
Read problems very carefully. If you have any questions raise your hand.
The correct nal answer alone is not sucient for

Mathematics Department, UCLA T. Richthammer
spring 09, sheet 6 May 1, 2009
Homework assignments: Math 170B Probability, Sec. 1
52. Show that E(X ) = E(E(X |Y ) in the case that X, Y have a joint PDF. Answer: Let f be the joint PDF, then fX (x|Y = y ) = so

Mathematics Department, UCLA T. Richthammer
spring 09, sheet 8 May 15, 2009
Homework assignments: Math 170B Probability, Sec. 1
78. Let Z1 , Z2 be independent standard normal, X1 = Z1 + Z2 +1, X2 = Z1 Z2 1. Calculate the expectation vector and the covaria

Mathematics Department, UCLA T. Richthammer
spring 09, midterm 1 Apr 27, 2009
Midterm 1: Math 170B Probability, Sec. 1
1. Let Z = X + Y , where X, Y are independent RVs with uniform distribution on [0, 1]. (a) Calculate E(Z ), V(Z ) and the PDF of Z . (b)

Mathematics Department, UCLA T. Richthammer
spring 09, midterm 2 May 18, 2009
Midterm 2: Math 170B Probability, Sec. 1
1. Let X, Y be continuous RVs. (a) What is the conceptual dierence between E(X |Y = y ) and E(X |Y )? (b) Give the denition of E(X |Y )

Midterm 1 practice, Math 170B - Lec 1, Spring 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) What is P()?
(b) (2 points) If X and Y are independent random variables and va

Midterm 1 practice, Math 170b - Lec 1, Spring 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) What is P()?
Solution: P() = 0.
(b) (2 points) If X and Y are independent rand

Midterm 1 practice, Math 170b - Lec 1, Spring 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().
(b) (2 points) If P(A) = 0.5, P(B ) = 0.4 a

Midterm 1 practice, Math 170b - Lec 1, Spring 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 1 practice, Math 170b - Lec 1, Spring 2013
Instructor: Toni Antunovi
c
c
Printed name:
Signed name:
Student ID number:
Instructions:
Read problems very carefully. If you have any questions raise your hand.
The correct nal answer alone is not suc

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.
From the books supplementary problems, solve problems 6