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Lecture - 1 Introduction to the Theory of Probability

Lecture - 2 Axioms of Probability

Lecture - 3 Axioms of Probability (Contd.)

Lecture - 4 Introduction to Random Variables

Lecture - 5 Probability Distributions and Density Functions

Lecture - 6 Conditional Distribution and Density Functions

Lecture - 7 Function of a Random Variable

Lecture - 8 Function of a Random Variable (Contd.)

Lecture - 9 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 (Contd.)

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 (Contd.)

Lecture - 21 Sequences of Random Variables

Lecture - 22 Sequences of Random Variables (Contd.)

Lecture - 23 Correlation Matrices and their Properties

Lecture - 24 Correlation Matrices and their Properties

Lecture - 25 Conditional Densities of Random Vectors

Lecture - 26 Characteristic Functions and Normality

Lecture - 27 Thebycheff Inquality and Estimation

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 Contd.

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)

Lecture - 40 Adaptive Filtering - LMS Algorithm

Description:

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, the 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.

Probability & Random Variables

NPTEL

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#Engineering #Electrical Engineering #Mathematics #Statistics & Probability #Signal Processing #Spectral Analysis #Probability Theory #Probability Distributions #Correlation #Covariance