Chapter 8
Response of Linear Systems to
Random Inputs
EE 385
Random Input
The previous discussions have been devoted to finding suitable
mathematical representations for random functions of time.
The next step is to see how these mathematical representa

Chapter 2
Random Variables
EE 385
David Pan
Outline
Concept of a Random Variable
Distribution Functions
Density Functions
Mean Values and Moments
The Gaussian Random Variable
Other Probability Density Functions
Examples and Applications
Concept of a Rando

Chapter 1
Introduction to Probability
EE 385
David Pan
Outline
Engineering applications of probability
Random experiments and events
Definitions of probability
The relative-frequency approach
Elementary set theory
The axiomatic approach
Conditional probab

EE 385
Pan
Homework 3
(Total 130 pts)
Due October 4, 2016 (Tuesday)
Note: You work must be typed using a word processor and submitted in printed
hardcopy form; handwritten homework will be discounted by 30%.
1. (20 pts) A Gaussian random current having ze

Chapter 4
Elements of Statistics
EE 385
David Pan
Introduction
Given an introductory study of probability and random
variables, we can look at some of the important
engineering applications of these concepts.
One such application is in the field of stat

EE 385
Pan
Homework 1
(Total 100 pts)
Due September 8, 2016 (Thursday)
Note: You work must be typed using a word processor and submitted in printed
hardcopy form; handwritten homework will be discounted by 30%.
1. (20 pts) A box contains 40 diodes of whic

Chapter 6
Correlation Functions
EE 385
David Pan
Statistical Description
Provide a statistical (rather than a probabilistic) description
of random processes.
A probabilistic description is the most complete one, since it
incorporates all the knowledge t

EE 385
Pan
Homework 2
(Total 70 pts)
Due September 22, 2016 (Thursday)
Note: You work must be typed using a word processor and submitted in printed
hardcopy form; handwritten homework will be discounted by 30%.
1. (20 pts) Problem 2-2.3 (pp. 110-111). For

Chapter 3
Several Random Variables
EE 385
David Pan
Outlines
Two Random Variables
Conditional Probabilities
Statistical Independence
Correlation between Random Variables
Density Function of the Sum of Two Random
Variables
The Characteristic Function
Moti

EE 385
Pan
Homework 4
(Total 120 pts)
Due Oct. 27, 2016 (Thursday)
Note: You work must be typed using a word processor and submitted in printed
hardcopy form; handwritten homework will be discounted by 30%.
1. (30 pts) Import two data sequences and into M

Chapter 7
Spectral Density
EE 385
Frequency-Domain Methods
The use of Fourier transforms and Laplace transforms in the analysis of
linear systems is widespread, since the convolution integral of timedomain methods is replaced by simple multiplication whe

Chapter 5
Random Processes
EE 385
David Pan
Definition
A random process is a collection of time functions and an associated
probability description.
The probability description may consist of the marginal and joint
probability density functions of all r