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Probability Foundation for Electrical Engineers

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. (from nptel.ac.in)

Lecture 06 - Properties of Probability Measures

Elementary properties, continuity of probability measures, nested events, the union bound.

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Lecture 01 - Introduction

Lecture 02 - Cardinality and Countability: Countable Sets, Countability of Rationals

Lecture 03 - Cardinality and Countability: Uncountable Sets, Cantor's Diagonal Argument

Lecture 04 - Probability Spaces 1

Lecture 05 - Probability Spaces 2

Lecture 06 - Properties of Probability Measures

Lecture 07 - Discrete Probability Spaces

Lecture 08 - Generated σ-Algebra, Borel Sets

Lecture 09 - Borel Sets and Lebesgue Measure 1

Lecture 10 - Borel Sets and Lebesgue Measure 2

Lecture 11 - The Infinite Coin Toss Model

Lecture 12 - Conditional Probability and Independence

Lecture 13 - Independence of Several of Events, Independence of σ-Algebras

Lecture 14 - The Borel-Cantelli Lemmas

Lecture 15 - Random Variables

Lecture 16 - Cumulative Distribution Function

Lecture 17 - Types of Random Variables

Lecture 18 - Continuous Random Variables

Lecture 19 - Continuous Random Variables (cont.), Singular Random Variables

Lecture 20 - Several Random Variables

Lecture 21 - Independent Random Variables 1

Lecture 22 - Independent Random Variables 2

Lecture 23 - Jointly Continuous Random Variables

Lecture 24 - Transformation of Random Variables 1

Lecture 25 - Transformation of Random Variables 2

Lecture 26 - Transformation of Random Variables 3

Lecture 27 - Transformation of Random Variables 4

Lecture 28 - Integration and Expectation 1

Lecture 29 - Integration and Expectation 2

Lecture 30 - Properties of Integrals

Lecture 31 - Monotone Convergence Theorem

Lecture 32 - Expectation of Discrete Random Variables, Expectation over Different Spaces

Lecture 33 - Expectation of Discrete Random Variables

Lecture 34 - Fatuous Lemma and Dominated Convergence Theorem

Lecture 35 - Variance and Covariance

Lecture 36 - Covariance, Correlation Coefficient

Lecture 37 - Conditional Expectation

Lecture 38 - MMSE Estimator Transforms

Lecture 39 - Moment Generating Function and its Properties

Lecture 40 - Characteristic Function 1

Lecture 41 - Characteristic Function 2

Lecture 42 - Concentration Inequalities

Lecture 43 - Convergence of Random Variables 1

Lecture 44 - Convergence of Random Variables 2

Lecture 45 - Convergence of Random Variables 3

Lecture 46 - Convergence of Characteristic Functions, Limit Theorems

Lecture 47 - The Laws of Large Numbers: Proofs of the Weak and Strong Laws

Lecture 48 - The Central Limit Theorem

Lecture 49 - A Brief Overview of Multivariate Gaussians