# Probability Foundation for Electrical Engineers

IIT Madras Course , Prof. Krishna Jagannathan

### Lecture 1: INTRODUCTION

##### Lecture Details :

Probability Foundation for Electrical Engineers by Dr. Krishna Jagannathan,Department of Electrical Engineering,IIT Madras.For more details on NPTEL visit http://nptel.ac.in

##### Course Description :

Preliminaries : Set Theory - Real Analysis basics - Cardinality and Countability,Probability Measures : Probability Spaces - Properties of Probability Measures - Discrete Probability Spaces - Borel Sets and Lebesgue Measure - Infinite Coin Toss Model - Conditional Probability and Independence - Borel-Cantelli Lemmas,Random Variables : RVs as measurable functions - Probability law, types of RVs, and CDF - Multiple Random Variables and Independence - Jointly Continuous Random Variables,Conditional Distributions - Sums of Random Variables - General Transformations of Random Variables, Jacobian formula

Integration and Expectation : Abstract Integration - Properties of Abstract Integrals - Monotone Convergence Theorem - Integration over Different Spaces - Integration of Continuous Random Variables,Radon-Nikodym theorem - Fatou's Lemma and Dominated Convergence Theorem - Variance and Covariance - Conditional Expectation and MMSE estimate,Transforms : Probability Generating Functions - Moment Generating Functions - Characteristic Functions - Inversion Theorem and Uniqueness of the Inversion - Concentration Inequalities,Limit theorems : Convergence of Random Variables and related theorems - Weak Law of Large Numbers - Strong Law of Large Numbers - Central limit theorem, Multi-variate Gaussian Distribution

##### Other Resources

IITMadras delivers the above video lessons under NPTEL program, there are more than 6000+ nptel video lectures by other IIT's as well.

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