Probability & Random Variables

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.