UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Fall 2014
Problem Set #9 Solutions
Problem 10.17
To the PSD of a discrete-time random process, SX (ej ) must

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Fall 2014
Problem Set #8 Solutions
Problem 9.18
a) Let V (k) be a zero-mean white noise process with unit va

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Fall 2014
Problem Set #6 Solutions
Problem 6.5
a) Since X is an exponential random variable with parameter ,

Homework 7 (EEC 161 - Spring 2014)
Name:
Student ID:
The grade scale is from 0 to 4:
4 Excellent: solved with no errors, shows perfect patronage of the concepts tested.
3 Good: some errors are present, but overall it shows that the understanding of the s

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Fall 2014
Midterm #1 Solutions
Problem 1
a) We have
F = (A + B.C).(D + E) .
b) Since the events Fu = A + B.C

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Fall 2014
Midterm #2 Solutions
Problem 1
a) The generating function of fX (x) is
MX (s) = E[esX ] =
esx fX (

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Fall 2014
Midterm Exam # 1 November 5, 2014
Instructions:
a) The exam is closed book, but you can use one 8

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EECl61 Probabilistic Analysis of Electrical and Computer Systems Fall 2014
Midterm Exam # 2 November 26, 2014
Instructions:
a) The exam is closed book, but you can use two 8

Problem 1: [all] points}
Consider the network shown in Fig. 1 connecting nodes 5 and R. The links :1, b, c, d
and r: are unreliable and can fail independently of one another, each with probabilityr ,0.
Let A, B, C, D and E be the events corresponding to t

Homework 1 (EEC 161 - Fall 2010)
Name:
Student ID:
The grade scale is from 0 to 4:
4 Excellent: solved with no errors, shows perfect patronage of the concepts tested.
3 Good: some errors are present, but overall it shows that the understanding of the sub

Homework 3 (EEC 161 - Fall 2011)
Name:
Student ID:
The grade scale is from 0 to 4:
4 Excellent: solved with no errors, shows perfect patronage of the concepts tested.
3 Good: some errors are present, but overall it shows that the understanding of the sub

Probability at the COHO
by Rahul Ramakrishnan
The Sample Space
1. Swirlz Bakery
2. Fickle Pickle Deli
3. Cook's
4. Ciao
5. Croutons
6. Tex Mex Grill
7. Chopstixx
Table of Contents
1. Sample Space
2. Restaurant Details
3. Conditional Variables
4. Condition

Homework 4 (EEC 161 - Fall 2011)
Name:
Student ID:
The grade scale is from 0 to 4:
4 Excellent: solved with no errors, shows perfect patronage of the concepts tested.
3 Good: some errors are present, but overall it shows that the understanding of the sub

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161 Probabilistic Analysis of Electrical and Computer Systems Spring 2015
Course Information
Course Content: Probabilistic and statistical methods for electrical and comp

Problem 1: {SCI points]
Consider an asymmetric Laplacian random variable X 1:Irith proll:ei.l:II'1l'1l'.:,-r density
iwr #20
gexpm] mail].
fxlmi = {
9.) Evaluate the moment generating function
Mxll = Elwpis-'il
of X. Sjpwooifl.r for what values of s it is

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Spring 2015
Problem Set #1 Solutions
Problem 2.2
b) Let A1 = cfw_a1 , a2 , a4 , A2 = cfw_a2 , a3 , a6 , and

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Spring 2017
Final Exam, Friday, June 9, 2017
Instructions:
a) The exam is closed book, but you can use three

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Spring 2017
Midterm #2 Solutions
Problem 1
a) The moment generating function of fY (y) is
Z
esy fY (y)dy
MY

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Spring 2017
Midterm Exam # 1 May 3, 2017
Instructions:
a) The exam is closed book, but you can use one 8 1/2

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Spring 2017
Midterm Exam # 2 May 24, 2017
Instructions:
a) The exam is closed book, but you can use two 8 1/

Random Variables (Discrete)
A random variable is a function that assigns a real number, X(s), to
each outcome s in the Sample Space of a random experiment.
Mapping, X(s) = x
S
s
x
real number line
For a discrete random variable, the mapping is to the set

Random Variables (Discrete)
A random variable is a function that assigns a real number,
X(s), to each outcome s in the Sample Space of a random
experiment.
Mapping, X(s) = x
S
s
real number line
x
3-1
M. Tummala & C. W. Therrien 2004
Example:
Roll a dice

Random Processes
Probability
Assignment
Outcome
Random
Experiment
X(s)
Sample
Space, S
Function of
Time
X(t, s)
Define Events
Concept of a random process (Ensemble)
Sample
Functions
experiments
1
t
X(t,s2)
2
t
t
t = t1
n
X(t,sn)
X(t,s1)
Time
(continuous

The Markov and Chebychev Inequalities
Pr [ X a ] = 1 Pr [ X < a ] = 1
a
f X ( x ) dx = 1 FX ( a )
What if not known?
Suppose we know only the mean and the variance of a r.v.
The mean and the variance do not always provide enough
information about the p

EEC161
Probabilistic Analysis of Electrical and Computer Systems
Spring 2017
where in the second line we have used the fact that since X1 and X2 are independent, their
covariance is zero.
b) Since X1 and X2 are independent, the pdf fX (x) of the sum X = X

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Spring 2017
Midterm #1 Solutions
Problem 1
a) Since the probability of each face is 1/6 and rolls are indepe

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161 Probabilistic Analysis of Electrical and Computer Systems Spring 2013
Midterm Exam # 2 May 22, 2013
Instructions:
a) The exam is closed book, but you can use two 8 1/

UNIVERSITY OF CALIFORNIA, DAVIS
Department of Electrical and Computer Engineering
EEC161
Probabilistic Analysis of Electrical and Computer Systems
Spring 2017
Final Exam Solutions
Problem 1
a) Since George keeps visting parts dealers until he finds the ri