ESE 520
Fall 2014
Old exam / practice problems for the final exam
1. Let X be a continuous random variable with distribution function F and density
f . Define a new random variable Y as Y = F (X). Show that Y is uniformly
distributed in the interval [0, 1

1
ESE 520 Final Practice
Zhenqi Lu
1. Are the following statements correct?
(a) Every subset of N is a Borel set.
Proof: Yes. Because for countable , it is always the natural way to take F to be the power set of N.
(b) Every subset of R is a Borel set.
Pr

ESE 520
Fall 2013
Homework 3
Due: Thursday, October 31, 2013
From the textbook, Probability and Random Processes for Electrical and Computer Engineers by John A.
Gubner, first edition, do the following 6 questions, each worth 5 points
Chapter 7
23, 27
Cha

ESE 520
Fall 2013
Homework 2
Due: Tuesday September 24, 2013
From the textbook, Probability and Random Processes for Electrical and Computer Engineers
by John A. Gubner, first edition, do the following 7 problems, each worth 5 points:
Chapter 1
54, 69
Cha

ESE 520
Fall 2013
Homework 6
Due: Tuesday, December 03, 2013
From the textbook, Probability and Random Processes for Electrical and Computer Engineers by John A.
Gubner, first edition, do the following 7 questions, each worth 5 points
Chapter 10
8, 17, 23

ESE 520
Fall 2013
Homework 5
Due: Thursday, November 14, 2013
From the textbook, Probability and Random Processes for Electrical and Computer Engineers by John A.
Gubner, first edition, do the following 6 questions, each worth 5 points
Chapter 3
20
Chapte

ESE 520
Fall 2013
Homework 1
Due: Tuesday September 10, 2013
From the textbook, Proability and Random Processes for Electrical and Computer Engineers by
John A. Gubner, first edition, do the following seven problems from Chapter 1. Each problem is
worth 5

ESE 520
Fall 2013
Homework 3
Due: Tuesday, October 8, 2013
From the textbook, Probability and Random Processes for Electrical and Computer Engineers by John A.
Gubner, first edition, do the following 7 problems, each worth 5 points:
Chapter 2
35
Chapter 4

ESE 520
Fall 2016
Probability and Stochastic Processes
Homework Set 1
due: Tuesday, September 13
From the textbook, Probability and Random Processes for Electrical and Computer
Engineers by John A. Gubner, first edition, do the following 10 problems from

ESE 520
Fall 2015
Probability and Stochastic Processes
Homework Set 5
due: Tuesday, November 3
From the textbook, Probability and Random Processes for Electrical and Computer
Engineers by John A. Gubner, first edition, do the following 5 problems, each wo

ESE 520
Fall 2015
Probability and Stochastic Processes
Homework Set 3
due: Tuesday, October 6
From the textbook, Probability and Random Processes for Electrical and Computer
Engineers by John A. Gubner, first edition, do the following 5 problems worth 5 p

ESE 520
Fall 2015
Probability and Stochastic Processes
Homework Set 2
due: Tuesday, September 22
From the textbook, Probability and Random Processes for Electrical and Computer
Engineers by John A. Gubner, first edition, do the following 6 problems, each

ESE 520
Fall 2015
Probability and Stochastic Processes
Homework Set 6
due: Tuesday, November 17
From the textbook, Probability and Random Processes for Electrical and Computer
Engineers by John A. Gubner, first edition, do the following 2 problems, each w

Two Proofs of the Central Limit Theorem
Yuval Filmus
January/February 2010
In this lecture, we describe two proofs of a central theorem of mathematics, namely the central limit theorem. One will be using cumulants, and the
other using moments. Actually, o

ESE 520
Fall 2015
Probability and Stochastic Processes
Homework Set 4
due: Tuesday, October 20
From the textbook, Probability and Random Processes for Electrical and Computer Engineers by John
A. Gubner, first edition, do the following problems:
1. (10 po

ESE 520
Fall 2015
Some practice problems for the final exam
1. Are the following statements correct? A simple YES or NO will do, but read the statements
carefully.
(a) Every subset of N is a Borel set.
(b) Every subset of R is a Borel set.
(c) Uncorrelate

ESE 520
Fall 2015
Probability and Stochastic Processes
Homework Set 1
due: Tuesday, September 8
From the textbook, Probability and Random Processes for Electrical and Computer
Engineers by John A. Gubner, first edition, do the following six problems from

ESE 520
Fall 2016
Probability and Stochastic Processes
Homework Set 2
due: Tuesday, September 27
From the textbook, Probability and Random Processes for Electrical and Computer
Engineers by John A. Gubner, first edition, do the following 6 problems, each