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# 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.

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