Capital University of Science & Technology

# Probability and Random Variables (EE2413)

##### Pre-requisite(s)

Calculus and Analytical Geometry (MT-1013)

Linear Algebra (MTC-1033)

##### Recommended Book(s)

Probability And Stochastic Processes by Roy D. Yates & David J. Goodman, John Wiley and Sons Inc., 2000

##### Reference Book(s)

Schaum's Outline of Theory And Problems of Probability, Random Variables, and Random Processes by Hwei P. Hsu,

## Course Objectives

The main aim of this course is to help the students to learn the basic ideas of the theory of probability and random signals. The theoretical part is supported by the examples of applicable nature especially from the areas of Electrical Engineering. The course will help students to aptly deal with the problems of probability and random functions later in their engineering degree program when the study various core courses like Digital Communications, Mobile Communications etc.

## Course Learning Outcomes (CLO)

CLO:1. Define theory of probability and random signals, illustrate the use of CDFs, PDFs and PMFs of continuous as well as discrete nature (Level: C1)

CLO:2. Transform given information to PMFs, PDFs and CDFs and express probability of events from statistical data. Moreover the students should be able to compare and correlate multiple random variables and evaluate if they are independent, orthogonal or correlated. (Level: C2)

CLO:3. Apply knowledge of probability to solve problems from the field of electronic, electrical and communications of applicable nature, falling in both discrete and continuous domain.  (Level: C3)

## Course Contents

##### Fundamental Concepts of Probability
• Set Operation
• Sample Space
• Events and Probabilities
• Probability Axioms
• Conditional Probability
• Independence
• Bayes’ Theorem
##### Discrete Random Variables
• Probability Mass Function
• Bernoulli, Geometric, Binomial and Poisson Random Variable
• Variance and Standard Deviation
• Conditional Probability Mass Function
##### Continuous Random Variables
• CDF of Continuous Random Variables
• Probability density function
• Expected Value
• Uniform, Gaussian, Standard Normal Random Variables
•  Probability Models
• Conditional Expected Values of Continuous Random Variables
##### Pairs of Random Variables
• Joint CDF
• Joint PMF
• Marginal PMF
• Joint PDF
• Functions of Two Random Variables
• Covariance
• Correlation
• Relation of Eigen values and Eigen vectors of Covariance Matrix
• Orthogonal and Uncorrelated Random Variables
• Conditional Joint PDF
• Bivariate Gaussian Random Variables

## Mapping of CLOs to Program Learning Outcomes

 CLOs/PLOs CLO:1 CLO:2 CLO:3 PLO:1 (Engineering Knowledge) √ √ PLO:2 (Problem Analysis) √ PLO:3 (Design and Development of Solutions) PLO:4 (Investigation) PLO:5 (Modern Tool Usage) PLO:6 (The Engineer and Society) PLO:7 (Environment and Sustainability) PLO:8 (Ethics) PLO:9 (Individual and Team Work) PLO:10 (Communication) PLO:11 (Project Management) PLO:12(Life Long Learning)