4EC2A RANDOM VARIABLES & STOCHASTIC PROCESSES
  Units    Contents of the subjects
I
PROBABILITY - Introduction, definitions, set theory, probability space, conditional probability, combined experiments.
II
RANDOM VARIABLES -Introduction, Distribution and density functions, Discrete and continuous random variables, Specific distributions: Normal (Gaussian), Exponential, Rayleigh, Uniform, Bernoulli, Binominal, Poisson, discrete Uniform and conditional distributions. Functions of one random variable: distribution, mean, variance, moments and characteristics functions.
III
MULTIPLE RANDOM VARIABLES -Two random variables: bivariate distributions, Pne function of two random variables, Two functions of two random variables, Joint moments, Joint characteristics functions, Conditional distributions, conditional expected values, statistical independence. Multiple random variables: multiple functions of multiple random variables, jointly Gaussian random variables, sums of random variable, Central limit theorem.
IV
STOCHASTIC PROCESSES - Definitions, Random process concept, Statistics of stochastic processes: mean, autocorrelation, autocovariance. Stationary processes, strict and wide sense stationary, Random processes and Linear Systems.
V
STOCHASTIC PROCESSES IN FREQUENCY DOMAIN - Power spectrum of stochastic processes, Transmission over LTI systems, Gaussian and White processes, Properties of power spectral density.
Text/References:
1. Probability, Random Variables And Stochastic Processes, Papoulis, TMH
2. Devore – Probability and statistics for engineering and sciences, Cengage learning
3. Mendenhall – Introduction to probability and statistics, Cengage learning
4. Probability, Random Variables And Random Signal Principles, Peebles, TMH
5. Probability Theory and Stochastic Processes for Engineers, Bhat, Pearson
6. Probability and Random Processes with Application to Signal Processing, 3/e, Stark, Pearson
7. Random Variables & Stochastic Processes, Gaur and Srivastava, Genius publications
8. Random Processes: Filtering, Estimation and Detection, Ludeman, Wiley
9. An Introduction to Probability Theory & Its App., Feller, Wiley
10. Stochastic Processes, 2ed, Ross, Wiley