University of Management & Technology
School of Science & Technology
Department of Electrical Engineering
EE 306 Probability and Statistics for Engineers
Lecture
Schedule
As per timetable on EED Website
Pre-requisite
None
Saleem Ata
Instructor(s)
2nd Floor
Office
Semester
Spring 2013
Credit Hours
3
Contact
saleemata@umt.edu.pk
Office Hours
See office door or EED Website
Course
Description
The course is a basic core course in Electrical Engineering which shall build necessary
background for courses in the area of communication. Course will include in-depth
knowledge of Basic Probability Theory, Discrete and Continuous Random Variables,
Functions of Random Variables, Expectations, Joint Distributions, Moment generating
functions. The course directly contributes to objectives a, d, e and f of the HEC Electrical
Engineering Curriculum.
Expected
Outcomes
Upon completion of this course, students will:
Students shall be able to use probability concepts and random variables as a tool to model
and solve practical problems with applications in Engineering.
The course strongly supports expected outcomes a, b, d, I and p of the HEC Electrical
Engineering Curriculum.
Required:
Textbook(s)
Grading
Policy
 Intuitive Probability and Random Processes using Matlab, Steven M. Kay.
Reference:
 A First course in Probability By Sheldon Ross
 Probability, Statistics, and Random Processes for Electrical Engineering By Alberto
Leon Garcia
 Homeworks : 10%
30% Submission, 70% in class quiz from Homework questions
 Quizzes : 15% (All Announced)
All quizzes will be announced. Quizzes will be 10-15 minutes. Quizzes could be open
book or closed book. All are advised to bring their text books along.
 Midterm : 25%
60-70 minute exam. All topics covered before the midterm exam will be included.
 Final : 50%
120-150 minute exam. Will be comprehensive.
Course Schedule
Lecture
1
3
4
4
2
2
4
Topics
Introduction to Probability
Probabilistic Modeling
Real-World Examples – Digital Communications
Basic Probability
Review of Set Theory
Combinatorics
Real World Example – Quality Control
Basic Probability theory
Conditional Probability
Joint Events
Statistically Independent Events
Bayes’ Theorem
Multiple Experiments
Real World Example – Cluster Recognition
Discrete Random Variables
Probability of Discrete Random Variables
Probability Mass Functions
Transformation of Discrete Random Variables
Cumulative Distribution Function
Real World Example – Servicing Customers
Expected Values for Discrete Random Variables
Determining Averages from PMF
Expected Values of Some Important Random Variables
Expected Value for a Function of a Random Variable
Variance and Moments of a Random Variable
Characteristics Functions
Estimating Means and Variances
Real World Example – Data Compression
Multiple Discrete Random Variables
Jointly Distributed Random Variables
Marginal PMF’s and CDF’s
Independence of Multiple Random Variables
Transformation of Multiple Random Variables
Real World Example – Assembling Health Risks
Conditional Probability Mass Functions
Conditional Probability Mass Function
Joint, Conditional and Marginal PMF’s
Mean of the Conditional PMF
Real World Example – Modeling Human Learning
Textbook (TB) /
Reference (Ref)
Readings
TB Chap 1
TB Chap 3
TB Chap 4
TB Chap 5
TB Chap 6
TB Chap 7
TB Chap 8
3
Continuous Random Variables
Definition of a Continuous Random Variable
PDF & Its Properties
Important PDF’s
Cumulative Distribution Function
Transformations
Mixed Random Variables
Real World Example – Setting Clipping Levels
TB Chap 10
2
Expected Values for Continuous Random Variables
Determining the Expected Value
Expected Values for Important PDF’s
Expected Value for a Function of Random Variable
Variance Moments
Characteristic Functions
Probability, Moments & Chebyshev Inequality
Estimating the Mean and Variance
Real World Example – Critical Software Testing
TB Chap 11
3
Multiple Continuous Random Variables
Jointly Distributed Random Variables
Marginal PDF’s and Joint CDF
Independence of Multiple Random Variables
Transformations
Expected Values
Joint Moments
Joint Characteristic Functions
Real World Example – Optical Character Recognition
TB Chap 12
2
Conditional Probability Density Functions
Conditional PDF
Joint, Conditional and Marginal PDF’s
Mean of Conditional PDF
Real World Example – Retirement Planning
TB Chap 13
Final Term Exam (Comprehensive)