4EC5 RANDOM VARIABLES & STOCHASTIC PROCESSES

UNIT 1

:

PROBABILITY

:Definitions, sample, space & events, joint & conditional

probability,dependent events.

UNIT 2

:

RANDOM VARIABLES :

Introduction, distribution & density functions, discrete & continuous

random  variables, special distributions : binominal, poisson, uniform, exponential, normal,  rayleigh.

conditional  distribution & density functions.

UNIT 3 : MULTIPLE RANDOM VARIABLES

:

Vector random variable, joint distribution functions, joint probability density function, conditional

distribution & density functions. Statistical independence, distribution & density function of sum of

random variable,  one function of one random variable ,one function of two random variable, two

function of two random variable.

UNIT 4 : OPERATION ON SINGLE & MULTIPLE RANDOM VARIABLES

:

Mean & variance, moments, chebyshev’s inequality, Central limit theorem, characteristic functions &

moment generating function, covariance & correlation coefficient of multiple random variable.

UNIT 5: STOCHASTIC PROCESSES

:

Introduction, random process concept, stationary & independence, ergodicity, correlation, functions.

Gaussion   Random Process, Transmission of Random process through linear systems. Power

spectral  Density, Cross Spectral density,