Axioms of probability-Conditional probability-Total probability-Baye’s theorem-Random variable – Probability mass function- Probability density functions -Moments - Moment generating functions and their properties.
Binomial- Poisson –Geometric – Uniform – Exponential-Gamma and Normal distributions and their properties.
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and Regression -Transformation of random variables - Central limit theorem.
Definition and examples - first order, second order, strictly stationary, wide-sense stationary and ergodic processes - Markov process - Binomial, Poisson and Normal processes - Sine wave process – Random telegraph process.
Auto correlation - Cross correlation - Properties – Power spectral density – Cross spectral density – Properties.
Reference Book:
1. Cooper. G.R.and Mc Gillem. C.D., "Probabilistic Methods of Signal and System Analysis", 3rd Indian Edition, Oxford University Press, New Delhi, 2012. (UNIT-I,II,III,IV,V) 2. Yates. R.D. and Goodman. D.J., "Probability and Stochastic Processes", 2nd Edition, Wiley India Pvt. Ltd., Bangalore, 2012. (UNIT-I,II,III)
Text Book:
1. Oliver C. Ibe, “Fundamentals of Applied probability and Random processes”, Elsevier, First Indian Reprint (2014) (UNIT-I,II,III) 2. Peebles Jr. P.Z., “Probability Random Variables and Random Signal Principles”, TataMcGraw-Hill Publishers, Fourth Edition, New Delhi, 2002. (UNIT-III,IV,V).