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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