Instructors: Kavitha Chandra, Joshua Levy

Introduction to theory and application of probability and random processes. Begins with review of sample space, field and probability measure and axiomatic definition of probability. Conditional probability and Bayes’ theorem. Continuous and discrete random variables and their probability distribution and density functions. Functions of random variables and their distribution and density functions. Expectation, variance and higher order moments. Characteristic and generating functions. Vector random variables and their applications. Maximum likelihood, mean-square estimation, regression analysis, orthogonality principle and central limit theorem. Introduction to random processes and conditions for stationarity and ergodicity. Correlation functions and spectral densities. Applications of linear systems with random process inputs. Statistics and estimators, confidence intervals, hypothesis testing.