Probability Foundation for Electrical Engineers

Instructor: Prof. Krishna Jagannathan, Department of Electrical Engineering, IIT Madras.

This is a graduate-level class on probability theory, geared towards students who are interested in a rigorous development of the subject. It is likely to be useful for students specializing in communications, networks, signal processing, stochastic control, machine learning, and related areas. In general, the course is not so much about computing probabilities, expectations, densities etc. Instead, we will focus on the 'nuts and bolts' of probability theory, and aim to develop a more intricate understanding of the subject. For example, emphasis will be placed on deriving and proving fundamental results, starting from the basic axioms.

Mod-01 Lec-01 INTRODUCTION.
Mod-01 Lec-02 CARDINALITY AND COUNTABILITY-1.
Mod-01 Lec-03 CARDINALITY AND COUNTABILITY-2.
Mod-01 Lec-04 PROBABILITY SPACES-1.
Mod-01 Lec-05 PROBABILITY SPACES-2.
Mod-01 Lec-06 PROPERTIES OF PROBABILITY MEASURES.
Mod-01 Lec-07 DISCRETE PROBABILITY SPACES.
Mod-01 Lec-08 GENERATED Σ-ALGEBRA, BOREL SETS.
Mod-01 Lec-09 BOREL SETS AND LEBESGUE MEASURE-1.
Mod-01 Lec-10 BOREL SETS AND LEBESGUE MEASURE-2.
Mod-01 Lec-11 THE INFINITE COIN TOSS MODEL.
Mod-01 Lec-12 CONDITIONAL PROBABILITY AND INDEPENDENCE.
Mod-01 Lec-13 INDEPENDENCE CONTD..
Mod-01 Lec-14 THE BOREL-CANTELLI LEMMAS.
Mod-01 Lec-15 RANDOM VARIABLES.
Mod-01 Lec-16 CUMULATIVE DISTRIBUTION FUNCTION.
Mod-01 Lec-17 TYPES OF RANDOM VARIABLES.
Mod-01 Lec-18 CONTINUOUS RANDOM VARIABLES.
Mod-01 Lec-19 CONTINUOUS RANDOM VARIABLES (CONTD.) AND SINGULAR RANDOM VARIABLES.
Mod-01 Lec-20 SEVERAL RANDOM VARIABLES.
Mod-01 Lec-21 INDEPENDENT RANDOM VARIABLES-1.
Mod-01 Lec-22 INDEPENDENT RANDOM VARIABES-2.
Mod-01 Lec-23 JOINTLY CONTINUOUS RANDOM VARIABLES.
Mod-01 Lec-24 TRANSFORMATION OF RANDOM VARIABLES-1.
Mod-01 Lec-25 TRANSFORMATION OF RANDOM VARIABLES-2.
Mod-01 Lec-26 TRANSFORMATION OF RANDOM VARIABLES-3.
Mod-01 Lec-27 TRANSFORMATION OF RANDOM VARIABLES-4.
Mod-01 Lec-28 INTEGRATION AND EXPECTATION-1.
Mod-01 Lec-29 INTEGRATION AND EXPECTATION-2.
Mod-01 Lec-30 PROPERTIES OF INTEGRALS.
Mod-01 Lec-31 MONOTONE CONVERGENCE THEOREM.
Mod-01 Lec-32 EXPECTATION OF DICRETE RANDOM VARIABLES, EXPECTATION OVER DIFFERENT SPACES.
Mod-01 Lec-33 EXPECTATION OF DICRETE RANDOM VARIABLES.
Mod-01 Lec-34 FATOU’S LEMMA & DOMINATED CONVERGENCE THEOREM.
Mod-01 Lec-35 VARIANCE AND COVARIANCE.
Mod-01 Lec-36 COVARIANCE, CORRELATION COEFFICIENT.
Mod-01 Lec-37 CONDITIONAL EXPECTATION.
Mod-01 Lec-38 MMSE ESTIMATOR, TRANSFORMS.
Mod-01 Lec-39 MOMENT GENERATING FUNCTION.
Mod-01 Lec-40 CHARACTERISTIC FUNCTION – 1.
Mod-01 Lec-41 CHARACTERISTIC FUNCTION – 2.
Mod-01 Lec-42 CONCENTRATION INEQUALITIES.
Mod-01 Lec-43 CONVERGENCE OF RANDOM VARIABLES – 1.
Mod-01 Lec-44 CONVERGENCE OF RANDOM VARIABLES – 2.
Mod-01 Lec-45 CONVERGENCE OF RANDOM VARIABLES – 3.
Mod-01 Lec-46 CONVERGENCE OF CHARCTERISTIC FUNCTIONS, LIMIT THEOREMS.
Mod-01 Lec-47 THE LAWS OF LARGE NUMBERS.
Mod-01 Lec-48 THE CENTRAL LIMIT THEOREM.
Mod-01 Lec-49 A BRIEF OVERVIEW OF MULTIVARIATE GAUSSIANS.