Advanced Probability Theory

Overview

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The course introduces the concept of probability through Kolmogorov’s Axioms. It develops the concept of probability density function, cumulative distribution function, and introduces the concept of a random variable. Different theoretical probability distributions, both discrete and continuous are introduced, and their properties are studied. Different generating functions, viz. MGF, PGF, and characteristic functions of different variables are discussed. It also introduces functions of one or two random variables and derived random variables, such as t, chisq, F are studied in detail. The concept of Order Statistics is introduced, and derivation of distribution of range, median etc. are discussed. Different limit theorems are discussed in detail.

Syllabus

Advanced Probability Theory (Lec 01).
Advanced Probability Theory (Lec 02).
Advanced Probability Theory (Lec 03).
Advanced Probability Theory (Lec04).
Advanced Probability Theory (Lec05).
Advanced Probability Theory (Lec06).
Advanced Probability Theory (Lec07).
Advanced Probability Theory (Lec08).
Advanced Probability Theory (Lec09).
Advanced Probability Theory (Lec10).
Advanced Probability Theory (Lec11).
Advanced Probability Theory (Lec12).
Advanced Probability Theory (Lec13).
Advanced Probability Theory (Lec14).
Advanced Probability Theory (Lec15).
Advanced Probability Theory (Lec16).
Advanced Probability Theory (Lec17).
Advanced Probability Theory (Lec18).
Advanced Probability Theory (Lec19).
Advanced Probability Theory (Lec20).
Advanced Probability Theory (Lec21).
Advanced Probability Theory (Lec22).
Advanced Probability Theory (Lec23).
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