Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #1
Due at the start of class: September 2.
Read Chapter 1.
Homework Policy: You are encouraged to work with others on the homeworks with the
following caveats.
Caveat 1: You write your o

Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #10
Due in class: November 20
Start reading Chapter 7.
1. The following questions are variations from an exam. For each sequence, compute the limit
if it exists. Also indicate which (if a

Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #8
Due in class: November 6
Read Chapter 6.
1. Let X = (X1 , X2 , . . . , X5 )T be a random vector whose components satisfy equations: Xi =
Xi1 + Bi , where the Bi , 1 i 5 are jointly ind

Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #3
Due in class: September 18
Finish reading Chapter 2, start reading Chapter 3.
1. Given the following distribution function:
2 +y 2
fXY (x, y) =
1 x
e
0
2
if xy 0
otherwise
(a) Show tha

Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #5
Due in class: October 2
Read Chapter 4.
1. A machine cuts rectangular plates with sides of length X and Y . Compute the the plates
expected area and perimeter length in terms of X , Y

Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #2
Due in class: September 9
Read Chapter 2.
1. Problem 1.32 in the text.
2. Compute the following with the aid of a calculator (i.e. if you think you need a computer
program you are doin

Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #9
Due in class: November 13
Finish reading Chapter 6.
1. Let X[n] be randomly shifted versions of the sequence 1,1,-1,-1,1,1,-1,-1,. . . , i.e. for uniform
random variable r cfw_0, 1, 2,

Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #6
Due in class: October 9
Read Chapter 5, sections 13.
1. The Erlang density is given for > 0 and positive integer n:
fX (x) =
n xn1 ex
(n1)!
0
x0
otherwise
When n = 1 we have the specia

Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #12
Due in class: December 11
Read Chapter 7 and sections 4.8 and 8.4.
1. Consider Z(t) = X(t) + N (t) where X(t) and N (t) are WSS and mutually uncorrelated with
power spectral densities

Midterm
ECE
ECEN 5612, Fall 2007
Noise and Random Processes
Prof. Timothy X Brown
October 23
CU Boulder
NAME:
CUID:
You have 120 minutes to complete this test.
Closed books and notes. No calculators. If you can not do a calculation by
hand, set up the c

Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #7
Due in class: October 30
Finish reading Chapter 5.
1. A doctor wants to survey whether men have a certain embarrassing condition. The procedure
is as follows. The doctor asks a patient

Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #4
Due in class: September 25
Finish reading Chapter 3. Read 4.14.4.
1. Let X N (0, 1) and let Y = g(X) where
g(x) =
0
x0
x 0<x1
1 x>1
(It may help to sketch g(x).) Compute FY (y) and f

Noise and Random Processes, TLEN 5612, TX Brown, Fall 2008
Homework #11
Due in class: December 4
Read Chapter 7.
a2
a1
x(t)
w1
- w2 -
w3
a4
-w4-
.
t
0
a3
The problems in this homework are based on a prelim exam question and the picture above.
A random pro