Probability & Random Variables

Overview

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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.

Syllabus

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.