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Probability and Random Processes

Probability and Random Processes. Instructor: Prof. Mrityunjoy Chakraborty, Department of Electronics and Electrical Communication Engineering, IIT Kharagpur. This course covers lessons on Introduction to probability, Random variables, Sequence of random variables and convergence, and Random process. Topics covered include axioms of probability, the concepts of random variables, function of a random variable, mean and variance of a random variable, moments, characteristic function, two random variables, joint moments, joint characteristic functions, sequences of random variables, random process, spectral analysis, spectral estimation, and mean sequence estimation. (from nptel.ac.in)

Lecture 15 - Correlation Covariance and Related Innver

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Lecture 01 - Introduction to the Theory of Probability

Lecture 02 - Axioms of Probability

Lecture 03 - Axioms of Probability (cont.)

Lecture 04 - Introduction to Random Variables

Lecture 05 - Probability Distributions and Density Functions

Lecture 06 - Conditional Distribution and Density Functions

Lecture 07 - Function of a Random Variable

Lecture 08 - Function of a Random Variable (cont.)

Lecture 09 - Mean and Variance of a Random Variable

Lecture 10 - Moments

Lecture 11 - Characteristic Function

Lecture 12 - Two Random Variables

Lecture 13 - Function of Two Random Variables

Lecture 14 - Function of Two Random Variables (cont.)

Lecture 15 - Correlation Covariance and Related Innver

Lecture 16 - Vector Space of Random Variables

Lecture 17 - Joint Moments

Lecture 18 - Joint Characteristic Functions

Lecture 19 - Joint Conditional Densities

Lecture 20 - Joint Conditional Densities (cont.)

Lecture 21 - Sequences of Random Variables

Lecture 22 - Sequences of Random Variables (cont.)

Lecture 23 - Correlation Matrices and their Properties

Lecture 24 - Correlation Matrices and their Properties (cont.)

Lecture 25 - Conditional Densities of Random Vectors

Lecture 26 - Characteristic Functions and Normality of a Random Vector

Lecture 27 - Chebyshev Inequality and Estimation of an Unknown Parameter

Lecture 28 - Central Limit Theorem

Lecture 29 - Introduction to Stochastic Process

Lecture 30 - Stationary Processes

Lecture 31 - Cyclostationary Processes

Lecture 32 - System with Random Process at Input

Lecture 33 - Ergodic Processes

Lecture 34 - Introduction to Spectral Analysis

Lecture 35 - Spectral Analysis (cont.)

Lecture 36 - Spectrum Estimation - Non-parametric Methods

Lecture 37 - Spectrum Estimation - Parametric Methods

Lecture 38 - Autoregressive Modeling and Linear Prediction

Lecture 39 - Linear Mean Square Estimation - Wiener (FIR) Filter

Lecture 40 - Adaptive Filtering - LMS Algorithm