# InfoCoBuild

## 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)

 Introduction to the Theory of Probability

 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

 References 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.