Stochastic Processes, Math 171, Spring 2015 - Homework 5
Due Friday May 1st
Read sections 1.5 and 1.6 in the book.
Solve problems 1.13, 1.14, 1.30, 1.34, 1.41, 1.49, 1.50 and 1.51 in the book.
Also so
Stochastic Processes, Math 171, Spring 2015 - Homework 3
Due Friday April 17th
Read section 1.3 in the book.
Solve problems 1.6 and 1.8 on pages 75/76 in the book.
Also solve the following.
Problem 1.
Stochastic Processes, Math 171, Spring 2015 - Homework 3
Due Friday April 17th
Read section 1.3 in the book.
Solve problems 1.6 and 1.8 on pages 75/76 in the book.
Also solve the following.
Problem 1.
Midterm 1, Math 171 - Spring 2015
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.
T
Stochastic Processes, Math 171, Spring 2015 - Homework 6
Due Friday May 8th
Read sections 1.8 and 1.9 in the book.
Solve problems 1.56, 1.57, 1.59, 1.60, 1.62, 1.64, 1.65 and 1.69 in the book.
And pro
Stochastic Processes, Math 171, Spring 2015 - Homework 6
Due Friday May 8th
Read sections 1.8 and 1.9 in the book.
Solve problems 1.56, 1.57, 1.59, 1.60, 1.62, 1.64, 1.65 and 1.69 in the book.
And pro
Midterm 2, Math 171, Spring 2015
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.
Th
Stochastic Processes, Math 171, Spring 2015 - Homework 1
Due Friday April 10th
Read section 1.1, 1.2 and 1.3 in the book.
Solve problems 1, 2, 3, 5 and 7 on page 75 in the book and 45 from page 84.
Al
Practice Final, Math 171 - Spring 2015
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
Practice Final, Math 171 - Spring 2015
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
Math 171, Spring 2015 - Homework 1
Due Friday April 3rd
Problem 1. Let X be a random variable with expectation 0 and variance 1.
Compute E[X 2 + X].
Solution: Since E(X 2 ) = var(X) + (EX)2 = 1 + 02 =
Math 171, Spring 2015 - Homework 1
Due Friday April 3rd
Problem 1. Let X be a random variable with expectation 0 and variance 1.
Compute E[X 2 + X].
Problem 2. Let X be a Poisson random variable with
Downloaded 11/20/15 to 137.189.170.231. Redistribution subject to SIAM license or copyright; see http:/www.siam.org/journals/ojsa.php
book
2011/6/7
page 25
Chapter 2
Random Variables and
Stochastic Pr
i
i
Downloaded 08/24/15 to 149.171.67.164. Redistribution subject to SIAM license or copyright; see http:/www.siam.org/journals/ojsa.php
i
book
2011/6/7
page 119
i
Chapter 4
Least Squares, the
Orthogo
Downloaded 10/15/15 to 150.135.239.97. Redistribution subject to SIAM license or copyright; see http:/www.siam.org/journals/ojsa.php
book
2011/6/7
page 81
Chapter 3
Conditional Expectations
and Discre
171 Midterm 2 Solutions, Winter 20171
1. Question 1
Let = [0, 1]. Let P be the uniform probability law on . Let X : [0, 1] R be a random
variable such that X(t) = t3 for all t [0, 1]. Let
A = cfw_[0,
Math 171, Fall 2016, UCLA
Name:
Instructor: Steven Heilman
UCLA ID:
Date:
Signature:
.
(By signing here, I certify that I have taken this test while refraining from cheating.)
Final Exam
This exam con
Math 171, Stochastic Processes, Winter 2017
Exterior Course Website: http:/www.math.ucla.edu/heilman/171w17.html
Prerequisite: Math 33A and Math 170A (or Statistics 100A). It is helpful, though not re
Math 171, Fall 2016, UCLA
Name:
Instructor: Steven Heilman
UCLA ID:
Date:
Signature:
.
(By signing here, I certify that I have taken this test while refraining from cheating.)
Mid-Term 1
This exam con
171 Final Solutions, Fall 20161
1. Question 1
True/False
(a) Let cfw_N (s)s0 be a Poisson Process with parameter = 1. Then
N (4) N (3), N (3) N (2), N (2) N (1), N (1)
are all independent random varia
171 Midterm 1 Solutions, Fall 20161
1. Question 1
True/False
(a) Let be a universe. Let A1 , A2 ,S. . . . Then
FALSE. If A1 = and A2 = , then
i=1 Ai = , but = cfw_x : positive integers j, x
Aj .
(b)
Math 171, Fall 2016, UCLA
Name:
Instructor: Steven Heilman
UCLA ID:
Date:
Signature:
.
(By signing here, I certify that I have taken this test while refraining from cheating.)
Mid-Term 2
This exam con
Stochastic Processes, Math 171, Spring 2015 - Homework 3
Due Friday April 24th
Read section 1.4 in the book.
Solve problems 1.9, 1.10, 1.11 and 1.12 on pages 76/77 in the book.
Also solve the followin
Stochastic Processes, Math 171, Spring 2015 - Homework 9
Due Friday May 29th
Read section 4.1, 4.2 and 4.3 in the book.
Solve problems 4.3, 4.4, 4.5 and 4.6 from the book, and the following problems.
Practice Midterm 1, Math 171, Spring 2015
Instructor: Toni Antunovi
c
c
Printed name:
Signed name:
Student ID number:
Instructions:
Read problems very carefully. If you have any questions raise your
i
Essentials of Stochastic Processes
Rick Durrett
70
10Sep
60
10Jun
10May
50
atexpiry
40
30
20
10
0
500
520
540
560
580
600
620
640
660
680
Almost Final Version of the 2nd Edition, December, 2011
Copy
Mathematics 171 - Homework 3 : Due
Thursday, April 27, 2017.
Feel free to use the results in the homework problems (including previous
homework problems). In other words, you may utilize the problems
Mathematics 171 - Homework 1 : Due
Thursday, April 13, 2017.
Problems 1.1, 1.2, 1.3, 1.5, 1.7 on Page 62-63 in the textbook.
A1. Let A, B be events in a sample space. Let C1 , ., Cn be events such tha
Mathematics 171 - Homework 2 : Due
Thursday, April 20, 2017.
Problems 1.8 (a) (c), 1.9 (a) 1.10 (b). on Page 63-64 in the textbook.
Some of the following problems come from the first edition of the te