Experiments, sample space, Events, Axioms, Assigning probabilities, Joint and conditional probabilities, Baye’s Theorem, Independence, Discrete Random Variables,Engg Example.
CDF, PDF,Gaussian random variable, Uniform Exponential, Laplace, Gamma, Erlang, Chi-Square, Raleigh, Rician and Cauchy types of random variables.
Expected value, EV of Random variables, EV of functions of Random variables, Central Moments, Conditional expected values.
Characteristic functions, Probability generating functions, Moment generating functions, Engg applications, Scalar quantization, entropy and source coding.
Pairs of Random variables, Joint CDF, joint PDF, Joint probability mass functions, Conditional Distribution, density and mass functions, EV involving pairs of Random variables, Independent Random variables, Complex Random variables, Engg Application.
Joint and conditional PMF, CDF,PDF,.EV involving multiple Random variables, Gaussian Random variable in multiple dimension, Engg application, linear prediction.
Definition and characterization, Mathematical tools for studying Random Processes, Stationary and Ergodic Random processes,Properties of ACF.
Markov processes, Gaussian Processes, Poisson Processes, Engg application, Computer networks, Telephone networks.