1. Course Description

This course will provide a solid foundation on the theory of probability and
its application in real life. The course will be taught in English.

2. Required Textbook

D. Bertsekas & J.N. Tsitsiklis, "Introduction to Probability" 2nd edition,
2008, Athena Scientific

3. References Textbook

S. Ghahramani, "Fundamentals of Probability with Stochastic Processes" 3rd
edition, 2005, Pearson

S. Ross, "A First Course in Probability" 9th edition, 2013, Pearson

H. Stark & J.W. Woods, "Probability, Statistics, and Random Processes for
Engineers" 4th edition, Pearson


4. Teaching Method

Lectures

5. Syllabus and Schedule

Chap.1. Sample Space and Probability Sets, Probabilistic Methods,
Conditional Probability, Total Probability Theorem, Bayes’ Rule,
Independence, Counting

Chap.2. Discrete Random Variables, Probability Mass Functions, Functions of
Random Variables, Expectation, Mean, Variance, Multivariate Random
Variables, Conditioning, Independence

Chap.3. General Random Variables, Continuous Random Variables, Probability
Density Functions, Cumulative Distribution Functions, Normal Random
Variables, Multivariate Random Variables, Conditioning, Bayes’ Rule

Chap.4. Further Topics on Random Variables, Distribution of Functions of
Random Variables, Covariance and Correlation, Conditional Expectation,
Transforms, Sum of Random Variables

Chap.5. Limit Theorems, Markov and Chebyshev Inequalities, Weak and Strong
Laws of Large Numbers, Central Limit Theorem, Convergence in Probability

Chap.6. Introduction to Statistics, Maximum A Posteriori (MAP) Estimator,
Minimum Mean Square Error (MMSE) Estimator, Maximum Likelihood (ML)
Estimator, Binary Hypothesis Testing, MAP and ML Detectors

6. Course website

All course-related materials will be posted on iLMS system