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Course content |
- Introduction : Motivation for studying the course, revision of basic math required, connection between probability and length on subsets of the real line, probability-formal definition, events and $sigma$-algebra, independence of events, and conditional probability, sequence of events, and Borel-Cantell Lemma.
- Random Variables : Definition of random variables, and types of random variables, CDF, PDF and its properties, random vectors and independence, brief introduction to transformation of random variables, introduction to Gaussian random vectors.
- Mathematical Expectations : Importance of averages through examples, definition of expectation, moments and conditional expectation, use of MGF, PGF and characteristic functions, variance and k-th moment, MMSE estimation.
- Inequalities and Notions of convergence : Markov, Chebychev, Chernoff and Mcdiarmid inequalities, convergence in probability, mean, and almost sure, law of large numbers and central limit theorem.
- A short introduction to Random Process : Example and formal definition, stationarity, autocorrelation, and cross correlation function, definition of ergodicity.
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Texts/References |
- Robert B. Ash, Basic Probability Theory, Reprint of the John wiley & Sons, Inc., New York, 1970 edition.
- Sheldon Ross, A first course in probability, Pearson Education India, 2002
- Bruce Hayek, An Exploration of Random Processes for Engineers, Lecture notes, 2012
- D. P. Bertsekas and J. Tsitisklis, 'Introduction to Probability' MIT Lecture notes, 2000 (link: https://www.vfu.bg/en/e-Learning/Math--Bertsekas_Tsitsiklis_Introduction_to_probability.pdf)
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