ECE 3075 ASSIGNMENT NO. 11
DATE ASSIGNED: DATE DUE: REMINDER: Thursday April 12, 2007 Wednesday April 18, 2007 before 6:00pm, scanned, via email to chao@gatech.edu. No late homeworks accepted. Solutions will be mailed immediately after 6:00pm. Quiz 3 will
ECE 3075, Fall 2008
Homework #3
Due Monday September 15 in class
Reading: C&M Chapter 2
Using you class notes, prepare a 1-2 paragraph summary of what we talked about in class the
rst week. I do not want just a bulleted list of topics, I want you to use c
ECE 3075, Fall 2008
Homework #7
Due Friday October 31, in class
Reading: Cooper and McGillem, Chapter 4 and class notes
Using you class notes, prepare a 1-2 paragraph summary of what we talked about in class
in the last week. I do not want just a bulleted
ECE 3075, Fall 2008
Homework #4
Due Wednesday September 24, in class
Reading: C&M Chapter 3
Using you class notes, prepare a 1-2 paragraph summary of what we talked about in class
in the last week. I do not want just a bulleted list of topics, I want you
ECE 3075, Fall 2008
Homework #5
Due Friday October 3 in class
Reading: C&M Chapter 3
Using you class notes, prepare a 1-2 paragraph summary of what we talked about in class
in the last week. I do not want just a bulleted list of topics, I want you to use
ECE 3075, Fall 2008
Homework #6
Due Friday October 10, in class
Reading: Cooper & McGillem, Chapter 6
Using you class notes, prepare a 1-2 paragraph summary of what we talked about in class
in the last week. I do not want just a bulleted list of topics, I
ECE 3075, Fall 2008
Homework #8
Due Friday November 7, in class
Reading: Cooper and McGillem, Chapters 5 and 6
Using you class notes, prepare a 1-2 paragraph summary of what we talked about in class
in the last week. I do not want just a bulleted list of
ECE 3075, Fall 2008
Homework #9
Due Friday November 14, in class
Reading: Cooper and McGillem, Chapter 6
Using you class notes, prepare a 1-2 paragraph summary of what we talked about in class
in the last week. I do not want just a bulleted list of topics
SOLUTIONS TO ECE 3075 ASSIGNMENT NO. 2
PROBLEM 2.1. There are two coins in a bag: One red, one blue. Neither coin is fair. The red coin
comes up head twice as often as a tail, while the blue coin comes up head five times as
often as a tail. One of these t
SOLUTIONS TO ISYE 3770 ASSIGNMENT NO. 1
PROBLEM 1.1. Let the universe set S be the set of all integers. Consider three subsets:
let A be the set of all even integers;
let B be the set of all integers that are a multiple of 3;
let C be the set of all in
SOLUTIONS TO ECE 3075 ASSIGNMENT NO. 6
PROBLEM 6.1.
(a)
Suppose X and Y are independent.
Is it necessarily true that X 2 and Y 2 are independent? Explain.
Yes.
Knowing the value of Y 2 tells us nothing about the probabilities regarding X 2.
(b)
Suppose U
SOLUTIONS TO ECE 3075 ASSIGNMENT NO. 5
PROBLEM 5.1. Suppose that X and Y are a pair of random variables whose joint pdf is:
f(x, y) =
6e (2x+3y),
0,
(a)
for x 0, y 0
.
elsewhere
Are X and Y uncorrelated? Yes Explain.
By inspection we observe that the join
SOLUTIONS TO ECE 3075 ASSIGNMENT NO. 1
PROBLEM 1.1. Suppose we a roll fair die, so that the sample space is S = cfw_1, 2, 3, 4, 5, 6.
Define the even event by A = cfw_2, 4, 6.
(a)
Give an example of an event B such that P(A|B) < P(A).
One example is the o
ECE 3075, Fall 2008
Homework #11
Due Friday December 5, in class
Reading: Cooper and McGillem, Chapters 8 and 9
Using you class notes, prepare a 1-2 paragraph summary of what we talked about in class
in the last week. I do not want just a bulleted list of
ECE 3075, Fall 2008
Homework #2
Due Friday September 5, in class
Reading: C&M Chapter 2
Using you class notes, prepare a 1-2 paragraph summary of what we talked about in class the
rst week. I do not want just a bulleted list of topics, I want you to use c
ECE 3075 ASSIGNMENT NO. 10
DATE ASSIGNED: DATE DUE: Thursday April 5, 2007 Thursday April 12, 2007
PROBLEM 10.1. Let cfw_X, X, X, X be i.i.d. Erlang(, k) with = 1/8 and k = 2. 1 Find an exact expression for the pdf f ( x ) of the sample mean X = - iXi. X
ECE 3075 ASSIGNMENT NO. 8
DATE ASSIGNED: DATE DUE: Tuesday March 27, 2007 Thursday March 29, 2007
PROBLEM 8.1. Let U and V be i.i.d. N(0, 1). Find the moment generating function X( s ) for the product X = UV. PROBLEM 8.2. Let W and Z be i.i.d. Exp(1/2). L
ECE 3075 ASSIGNMENT NO. 9
DATE ASSIGNED: DATE DUE: Tuesday March 29, 2007 Thursday April 5, 2007
PROBLEM 9.1. A machine breaks down randomly, independent of all other breakdowns, and is repaired immediately once it breaks down. We assume that the time in
ECE 3075 ASSIGNMENT NO. 7
DATE ASSIGNED: DATE DUE: REMINDER: Thursday March 8, 2007 Wednesday March 14, 2007 before 6:00pm, scanned, via email to chao@gatech.edu. No late homeworks accepted. Solutions will be mailed immediately after 6:00pm. Quiz 2 will b
ECE 3075 ASSIGNMENT NO. 4 PICK ANY TWO OF THE FIVE PROBLEMS
DATE ASSIGNED: DATE DUE: READING: REMINDER: Tuesday February 13, 2007 Thursday February 15, 2007 Chapter 3 Quiz 1 will be Tuesday, February 20, open book and open notes.
PROBLEM 4.1. Let U Unifor
ECE 3075 ASSIGNMENT NO. 2
DATE ASSIGNED: DATE DUE: READING: Tuesday January 23, 2007 Tuesday January 30, 2007 Chapters 1 and 2
PROBLEM 2.1. Assume that a discrete random variable X has a probability p of being one, and a probability of 1 p of being a zero
ECE 3075 ASSIGNMENT NO. 3
DATE ASSIGNED: DATE DUE: READING: Tuesday February 6, 2007 Tuesday February 13, 2007 Chapters 2 and 3
PROBLEM 3.1. A Gaussian random variable with variance = 4 is positive with probability 0.2. Find its mean. PROBLEM 3.2. Suppose
ECE 3075 ASSIGNMENT NO. 6
DATE ASSIGNED: DATE DUE: READING: Thursday March 1, 2007 Thursday March 8, 2007 Chapter 3
PROBLEM 6.1. Two random variables X and Y are independent if and only if the region of support of the joint pdf is rectangular in shape. (a
ECE 3075
ASSIGNMENT NO. 5
DATE ASSIGNED:
DATE DUE:
READING:
Thursday February 22, 2007
Thursday March 1, 2007
Chapter 3
PROBLEM 5.1. An exponential RV X has pdf f( x ) = exu( x ), where u(x) is the unit step function.
If Pr[X > ln(2)] = 0.125, find .
PROB
ECE 3075 ASSIGNMENT NO. 1
DATE ASSIGNED: DATE DUE: READING: Tuesday January 16, 2007 Tuesday January 23, 2007 Chapter 1
PROBLEM 1.1. A sample space W = cfw_2, 4, 6, 8, 10, 12 has three subsets: A = cfw_2, 4, 6, B = cfw_8, 10, 12, and C = cfw_2, 4, 6, 12.
ECE 3075, Fall 2008
Homework #1
ECE 3075
ASSIGNMENT NO. 1
Due Friday August 29, in class
DATE ASSIGNED: Tuesday January 16, 2007
Reading:
DATE DUE: Cooper&McGillem, Chapter 1
Tuesday January 23, 2007
READING: class notes, prepare a 1-2 paragraph summary o
ECE 3075, Fall 2008
Homework #10
Due Wednesday November 26, in class
Reading: Cooper and McGillem, Chapter 7
Using you class notes, prepare a 1-2 paragraph summary of what we talked about in class
in the last week. I do not want just a bulleted list of to
SOLUTONS TO ECE 3075 ASSIGNMENT NO. 4
PROBLEM 4.1. Find the probability that the roots of the polynomial x2 + Bx + 1 are complex
valued, assuming that the coefficient B is chosen randomly according to the following
pdf:
f( b ) = | b |eb
-3
-2
-1
0
2
1
2
3
SOLUTIONS TO ECE 3075 ASSIGNMENT NO. 3
PROBLEM 3.1. For each of the distributions identified below, find that the probability that a random
variable X with that distribution falls within the interval 1 < X < 4.
In other words, find P(1 < X < 4).
(a)
X Uni
GEORGIA INSTITUTE OF TECHNOLOGY
School of Electrical and Computer Engineering
EE 3340 B: Random Signals and Noise
Instructor: Dr. Guotong Zhou
Quiz 1
January 25, 1996
Name:
General Instructions
1. This is a 50 minute, closed book, closed notes exam. One 8