Continuous and discrete random variables and their joint probability distribution and density functions; Functions of one random variable and their distributions; Independent random variables and conditional distributions; One function of one and two random variables; Two functions of two random variables and their joint density functions; Jointly distributed discrete random variables and their functions; Characteristic functions and higher order moments; Covariance, correlation, orthogonality; Jointly Gaussian random variables; Linear functions of Gaussian random variables and their joint density functions. Stochastic processes and the concept of Stationarity; Strict sense stationary (SSS) and wide sense stationary (WSS) processes; Auto correlation function and its properties; Poisson processes and Wiener processes; Stochastic inputs to linear time-invariant (LTI) systems and their input-output autocorrelations; Input-output power spectrum for linear systems with stochastic inputs; Minimum mean square error estimation (MMSE) and orthogonality principle; Auto regressive moving average (ARMA) processes and their power spectra. Co-listed as BE 6453.
Prerequisite: Graduate status. *Online version available.