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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

Description:

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.

Probability Foundation for Electrical Engineers

NPTEL

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#Mathematics #Statistics & Probability #Engineering #Electrical Engineering #Probability Theory #Conditional Probability #Limit theorems #Covariance

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