Information Package / Course Catalogue - Adnan Menderes University

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Random Variables & Stochastic Process

Course Code	: EEE531
Course Type	: Area Elective
Couse Group	: Second Cycle (Master's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 6

Objectives of the Course

The main objective of this course is to understand the mathematical theory and to gain experience about the application areas of random variables and random processes.

Course Content

Review of probability theory: Conditional probability and independence, random variables, probability distribution and density, function of random variables, expectation and conditional expectation with their properties. Random processes: Continuous and discrete-time random processes, correlation function and power spectrum, Gaussian and Poisson processes, continuity of random processes, stationarity and wide-sense stationarity, white noise, ergodicity.

Name of Lecturer(s)

Learning Outcomes

1.	To identify and formulate the fundamental probability density and distribution functions, as well as functions of random variables.
2.	To explain the concepts of expectation and conditional expectation, and describe their properties.
3.	To understand and analyse continuous and discrete-time random processes
4.	To explain the concepts of stationarity and wide-sense stationarity, and appreciate their significance
5.	To employ the theory of stochastic processes to analyse linear systems
6.	Apply the above knowledge to solve basic problems in filtering, prediction and smoothing

Recommended or Required Reading

1.	Probability, Random Variables and Stochastic Processes, by Athanasios Papoulis and S. Unnikrishna Pillai, 4th Edition, McGraw Hill 2002
2.	Probability, Statistics and Random Processes for Electrical Engineering, by Alberto Leon-Garcia, 3rd Edition, Pearson, 2008.
3.	Introduction to Probability and Random Processes, by Jorge I. Aunon and V. Chandrasekar, McGraw Hill, 1997

Weekly Detailed Course Contents

Week 1 - Theoretical

Basic Concepts of Probability: Axiomatic definition, use of set concepts, conditional and joint probability.

Week 2 - Theoretical

Basic Concepts of Probability: Independence, Bayes Rule, Total Probability.

Week 3 - Theoretical

Random Variables: Basic concepts, The random variable concept, Distribution function, Density function.

Week 4 - Theoretical

Random Variables: The Gaussian random variable, other distribution and density examples, Conditional distribution and density functions

Week 5 - Theoretical

Operation on One Random Variable: Expectation, Functions of a Random Variable.

Week 6 - Theoretical

Operation on One Random Variable: Transformations of a random variable, Computer generation of one random variable.

Week 7 - Theoretical

Multiple Random Variables

Week 8 - Theoretical

Operations on Multiple Random Variables, Midterm Exam

Week 9 - Theoretical

Vector Random Variables

Week 10 - Theoretical

Operations on Vector Random Variables

Week 11 - Theoretical

Random Processes: The random process concept, Stationarity and independence, Correlation functions.

Week 12 - Theoretical

Random Processes: Measurement of correlation functions, Gaussian random processes, Poisson random process

Week 13 - Theoretical

Spectral Characteristics of Random Processes

Week 14 - Theoretical

Spectral Characteristics of Random Processes

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Attending Lectures	1	%2
Assignment	5	%8
Midterm Examination	1	%20
Final Examination	1	%70

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	1	3	56
Assignment	5	2	2	20
Individual Work	6	1	1	12
Midterm Examination	1	10	5	15
Final Examination	1	20	30	50
TOTAL WORKLOAD (hours)				153

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7
OÇ-1	4	4	4	4	4	4	4
OÇ-2	4	4	4	4	4	4	4
OÇ-3	4	4	4	4	4	4	4
OÇ-4	4	4	4	4	4	4	4
OÇ-5	4	4	4	4	4	4	4
OÇ-6	4	4	4	4	4	4	4

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