Lecture Notes || SNS Courseware

UNIT 1:

Discrete Random Variable

Continuous Random Variable

Moments

Moment generating functions and their properties.

Binomial Distribution

Poisson Distribution

Exponential Distribution

Normal Distribution

UNIT 2:

Joint distributions

Marginal distributions

Conditional distributions

Covariance

Correlation

Regression

UNIT 3:

Random Process

Stationary Process

Wide Sense Stationary Process

Ergodic Process

Markov Process

Markov Chain

Poisson process

UNIT 4:

Auto correlation

Cross correlation

Properties

Power spectral density

Cross spectral density

Properties

Wiener-Khintchine relation

UNIT 5:

Linear time invariant system

System transfer function

Linear system with random inputs

Auto correlation functions of input and output

Cross correlation functions of input and output

Lecture Notes