# Probability and Random Variables Syllabus ```University of Jordan
College of Engineering &amp; Technology
Department of Electrical Engineering
Second Term – A.Y. 2011-2012
Probability &amp; Random Variables (EE 0953321) (3 Cr. – Core Course)
Course:
Catalog Data: Probability, Random Variable, Operation on One Random Variable, Multiple
Random Variables, Operations on Multiple Random Variables, Random Processes,
Spectral Characteristics of Random Processes, linear systems.
Prerequisites by
Course:
Signals analysis and Systems
Prerequisites
By topic:
(EE 0903221)
Students are assumed to have a background of the following topics:
 Calculus skills.
 Solution of ordinary differential equations.
 Fourier transform
 Linear Systems
Textbook:
Probability, Random Variables, and Random Signal Principles;
Peyton Z. Peebles; McGraw-Hill, Inc. 4th Edition
References:
 Athanasios Papoulis. Probability ,Random Variables, and Stochastic
Processes,3rd Edition, Mc-Graw-Hill
 Probability and Random Processes for Electrical Engineers, Y. Viniotis,
WCB McGraw-Hill, 1998.
 Probability and Statistics for Engineering and the Sciences (6 th
Edition), by Jay L. Devore, 2004
 Lecture Notes and Handouts
Schedule &amp;
Duration:
16 Weeks, 48 lectures, 50 minutes each (including exams).
Minimum Student
Material:
Text book, class handouts, scientific calculator, and an access to a personal
computer.
Minimum College
Facilities:
Classroom with whiteboard, library, and computational facilities.
Course Objectives:
The course objectives are

Introduce the topics of probability, random variables, and stochastic processes at

to train the student to formulate such problems within the framework of probability
theory
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Course Outcomes and Relation to ABET Program Outcomes:
Upon successful completion of this course, a student should be able to::
1. Convert an Engineering statment problem into a precise mathematical probabilistic
Statement .
2. Use statistical principles and the properties of random variables to solve
Probabilistic problems .
3. Calculate standard statistics from mass, distribution and density functions .
4. Recognize , interpret and apply a variety of deterministic and nondeterministic random
Processes that occur in engineering .
5. Calculate the autocorrelation and spectral density of a random process and recognize the
relation beteen them..
6. Understand stochastic phenomena such as white and colored noise .
7. Understand linear systems. And their output charactaristics .
Course Topics:
Contact Hours
Topic
Description
T.1.
Probability:
Axiomatic definition, use of set concepts, conditional and joint probability,
independence, Bays Rule, Total Probability.
5
T.2.
Random Variables:
7
Basic concepts, The random variable concept, Distribution function, Density
function, The Gaussian random variable, other distribution and density
examples, Conditional distribution and density functions
Families of distributions.
T.3.
Operation on One Random Variable
7
Expectation, Moments, Functions that give Moments, Transformations of a
random variable, Computer generation of one random variable
T.4.
Multiple Random Variables
6
Vector random variables, Joint distribution and its properties, Joint density and
its properties, Conditional distribution and density, Statistical independence,
Distribution and density of a sum of random variables, Central limit theorem
T.5
Operations on Multiple Random Variables
6
T.6
Expected value of a function of random variables, Joint characteristic function,
Jointly Gaussian random variables, Transformations of multiple random
variables, linear transformation of Gaussian random variables, Computer
generation of multiple random variables
Random Processes
7
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The random process concept, Stationarity and independence, Correlation
functions, Measurement of correlation functions, Gaussian random processes,
Poisson random process
T.7
Spectral Characteristics of Random Processes
5
Power density spectrum and its properties, Relationship between power
spectrum and autocorrelation function, Cross-Power density spectrum and its
properties, Relationship between cross-power spectrum and cross-correlation
function , some noise definitions and other topics
T.8
5
Linear systems.
Input output relations of linear systems.
Computer Usage:
Course work including assignments using software packages, especially Matlab
Attendance:
Class attendance will be taken every class.
Assessments:
Exams, Quizzes, and Assignments.
First Exam
Midterm Exam
Final Exam
20 %
30 %
50 %
Total 100%
Instructor:
Last Updated:
Instructor Name
Office
Hasan Farahneh
EE dep 3rd
floor
Ext.
22862
E-mail
h.farahneh@ju.edu.jo
Feb 1, 2012
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