# Probability Foundations for Electrical Engineers – EE3110

**Title :** Probability Foundations for Electrical Engineers

**Course No :** EE3110

**Credits :** 4

**Prerequisite :**

**Syllabus :**

- Introduction to Probability: Sets, Events, Axioms of Probability, Conditional Probability and Independence, Bayes Theorem and MAP Decision Rule
- Random Variables: Definitions, Cumulative Distribution Functions, mass and density functions, joint and conditional distributions, Functions of Random Variables
- Expectations: Mean, Variance, Moments, Correlation, Chebychev and Schwarz Inequalities, Moment-generating and Characteristic Functions, Chernoff Bounds, Conditional Expectations
- Random Vectors: Jointly Gaussian random variables, Covariance Matrices, Linear Transformations, Diagonalization of Covariance Matrices
- Random Sequences: Sequences of independent random variables, correlation functions, wide-sense stationary sequences, LTI filtering of sequences
- Law of Large Numbers, Central Limit Theorem

**Text Books : **

- Stark and Woods: Probability and Random Processes with Applications to Signal Processing, 3rd ed 2002, Pearson Education

**References :**