MAT 501 PROBABILITY, RANDOM VARIABLES AND STOCHASTIC PROCESSES (4-0-0-4)
Probability theory: Review of Set theory; introduction to probability, axioms of probability; joint and conditional probability; Bayes theorem. Random Variables: The concept of a random variable (RV); continuous and discrete RVs; probability distribution and density functions, properties; some standard examples; Functions of an RV, distribution and densities of functions of an RV, examples; expected value/mean and variance; moments and characteristic functions; two RVs: joint distribution and density functions; correlation, covariance, orthogonality and independence; conditional distribution and density functions. Elements of Estimation theory: Estimation of mean and variance; Chebyshev inequality; Parameter Estimation, Properties of Estimators; Cramer-Rao bound. Stochastic Processes: Introduction, Statistics of stochastic processes, correlation and covariance; Stationarity; Autocorrelation, Power density spectrum, and Wiener Khinchin Theorem; Linear Systems with stochastic inputs.