1. Course Description
<br>
<br>This course will provide a solid foundation on the theory of probability and 
<br>its application in real life. The course will be taught in English.
<br>
<br>2. Required Textbook
<br>
<br>D. Bertsekas & J.N. Tsitsiklis, "Introduction to Probability" 2nd edition, 
<br>2008, Athena Scientific
<br>
<br>3. References Textbook
<br>
<br>S. Ghahramani, "Fundamentals of Probability with Stochastic Processes" 3rd 
<br>edition, 2005, Pearson
<br>
<br>S. Ross, "A First Course in Probability" 9th edition, 2013, Pearson
<br>
<br>H. Stark & J.W. Woods, "Probability, Statistics, and Random Processes for 
<br>Engineers" 4th edition, Pearson
<br>
<br>
<br>4. Teaching Method
<br>
<br>Lectures
<br>
<br>5. Syllabus and Schedule
<br>
<br>Chap.1. Sample Space and Probability Sets, Probabilistic Methods, 
<br>Conditional Probability, Total Probability Theorem, Bayes’ Rule, 
<br>Independence, Counting
<br>
<br>Chap.2. Discrete Random Variables, Probability Mass Functions, Functions of 
<br>Random Variables, Expectation, Mean, Variance, Multivariate Random 
<br>Variables, Conditioning, Independence
<br>
<br>Chap.3. General Random Variables, Continuous Random Variables, Probability 
<br>Density Functions, Cumulative Distribution Functions, Normal Random 
<br>Variables, Multivariate Random Variables, Conditioning, Bayes’ Rule
<br>
<br>Chap.4. Further Topics on Random Variables, Distribution of Functions of 
<br>Random Variables, Covariance and Correlation, Conditional Expectation, 
<br>Transforms, Sum of Random Variables
<br>
<br>Chap.5. Limit Theorems, Markov and Chebyshev Inequalities, Weak and Strong 
<br>Laws of Large Numbers, Central Limit Theorem, Convergence in Probability
<br>
<br>Chap.6. Introduction to Statistics, Maximum A Posteriori (MAP) Estimator, 
<br>Minimum Mean Square Error (MMSE) Estimator, Maximum Likelihood (ML) 
<br>Estimator, Binary Hypothesis Testing, MAP and ML Detectors
<br>
<br>6. Course website
<br>
<br>All course-related materials will be posted on iLMS system
<br>