KOM 505E - Probability Theory&Stochast.Pr

Course Objectives

Review basic concepts on probability and random variables. Understand generalization of random variable concept to random sequences and random processes. Learn specific types of random sequences and random processes. Analyze random sequences and processes in transform domain. Analyze output of linear time invariant systems to random sequences and inputs in time and transform domains.

Course Description

Random experiments, axioms of probability, techniques of counting,
conditional probability, independence, sequential experiments.
Random variables, probability distributions, some important random variables: Bernoulli, binomial, geometric, Poisson, uniform, exponential, Gaussian, gamma. Functions of random variables, expected values, Chebyshev inequality, characteristic functions.
Multiple random variables, joint cdf's and pdf's, independence, conditional probability and conditional expectation, functions of several random variables, expected values of functions of vector random variables, multidimensional Gaussian random variables.Sums of random variables, the law of large numbers, the central limit theorem.
Random processes, distributions, mean, autocorrelation, autocovariance, some important random processes: sum, binomial counting, random walk, Poisson,
Wiener, Brownian motion. Stationary random processes, derivatives and integrals
of random processes, time averages of random processes and ergodic theorems.
Power spectral density, response of linear systems to random signals.