HW # 1 Solution
ECES 522: Random Processes & Spectral Analysis
Winter AY 2013-2014
1. A Gaussian random process X [n] has zero mean and auto-correlation function
Rx [k ] =
7 |k| 1 |k|
2
+3
10
8
(1)
(a) Find the z-transform of Rx [k ] and nd its poles and

HW # 1
ECES 522: Random Processes & Spectral Analysis
Winter AY 2013-2014
1. A Gaussian random process X [n] has zero mean and auto-correlation function
Rx [k ] =
7 |k| 1 |k|
2
+3
10
8
(1)
(a) Find the z-transform of Rx [k ] and nd its poles and zeros.
(b

Steven Weber
Dept. of ECE
Drexel University
ECE-S521 Probability and random variables
Homework 4 due: 6pm Wednesday October 26, 2011
Instructions:
1. This page must be signed and stapled to your assignment. Homework handed in without this signed page
will

Steven Weber
Dept. of ECE
Drexel University
ECE-S521 Probability and random variables
Homework 3 due: 6pm Wednesday October 19, 2011
Instructions:
1. This page must be signed and stapled to your assignment. Homework handed in without this signed page
will

Steven Weber
Dept. of ECE
Drexel University
ECE-S521 Probability and random variables
Homework 1 due: 6pm Wednesday October 5, 2011
Instructions:
1. This page must be signed and stapled to your assignment. Homework handed in without this signed page
will

Steven Weber
Dept. of ECE
Drexel University
ECE-S521 Probability and random variables
Homework 2 due: 6pm Wednesday October 12, 2011
Instructions:
1. This page must be signed and stapled to your assignment. Homework handed in without this signed page
will

Lecture 6: Discrete Time Homogenous Markov Chains, IV:
Mean Time to Absorption & Absorption Probabilities
John MacLaren Walsh, Ph.D.
February 19, 2014
1
References
Markov chains are a widely taught subject, and hence there are a wide variety of texts. A f

Lecture 5: Discrete Time Homogenous Markov Chains, III:
Proofs of State Classication Properties & Limiting Behavior
John MacLaren Walsh, Ph.D.
February 12, 2014
1
References
Markov chains are a widely taught subject, and hence there are a wide variety of

Lecture 3: Discrete Time Markov Chains, Part 1
John MacLaren Walsh, Ph.D.
January 29, 2013
1
What are Markov Chains?
Recall that a Markov Process satises the property that the future is independent of the past given the
present. Formally, for any collecti

Practice problems: Exam # 1
ECES 522: Random Processes & Spectral Analysis
Winter AY 2013-2014
1. Given a random process X (t), dene for some constant another random process Y (t) as
Y (t) = X (t + ) X (t).
(1)
(a) Suppose X (t) is stationary. Will Y (t)

ECES 522, Homework # 5
due February 26 at 6pm
1. Find the mean amount of time it takes the monkey to unlock the computer in problem
2 of homework 3 by applying the mean time to absorption calculation. To do so,
assume that the computer enters a non-match

HW # 2
ECES 522: Random Processes & Spectral Analysis
Winter AY 2013-2014
You wish to estimate a zero mean WSSRP X [n] which you know to have the auto-correlation function
|k | = 2
1
35
|k | = 1
6
RXX [k ] =
k=0
31
3
0
otherwise
(1)
All that is availabl

HW # 3
ECES 522: Random Processes & Spectral Analysis
Winter AY 2013-2014
1. A Markov chain has a probability transition matrix
0.5 0.3 0.2
A = 0.1 0.15 0.75
0.2 0.45 0.35
(1)
(a) For each (i, j ) cfw_1, 2, 32 obtain an explicit expression (by utilizing

HW # 2
ECES 522: Random Processes & Spectral Analysis
Winter AY 2013-2014
You wish to estimate a zero mean WSSRP X [n] which you
1
35
6
RXX [k ] =
31
3
0
know to have the auto-correlation function
|k | = 2
|k | = 1
k=0
otherwise
(1)
All that is availabl

EE226: Random Processes in Systems
Fall06
Problem Set 1 Sept, 14
Lecturer: Jean C. Walrand GSI: Assane Gueye
This problem set essentially reviews notions of conditional expectation, conditional distribution, and Jointly Gaussian random variables. Not all