EE3110 – Probability Foundations

Set theory basics: sets, union, intersection, De Morgan's theorem, disjoint sets, eld, borel eld and their applications to probability theory.

Evolution of Probability Theory: Classical theory of probability, relative fre-quency de nition and their limitations. Modern theory of probability - probability space triplet. Axioms, borel set & elds and the case of sample space being countable & in nite and uncountable.

Probability Concepts: Conditional probability, total probability theorem and Bayes' rule, independence, permutations and combinations in probability

Random Variables: Discrete RVs, Bernoulli's RV, Binomial RV, probability mass function, continuous RVs, exponential, Gaussian, Rayleigh, Rician RVs, moments of a distribution, functions of RV, joint PMF, conditioning, independence

Bayes Theorem and its role in estimation : Covariance & correlation, conditional expectation, transforms, sum of a random number of independent RVs.

Limit Theorems: Markov & Chebyshev inequalities, weak law of large numbers, convergence in probability, strong law of large numbers. Poisson process & Short account of Bayesian statistical inference (time permitting)