Credits: 48credit hours.
Class Meetings: 16sessions / week
3hours / session
Knowledge of basic matrix analysis, continuous and discrete time signal and systems analysis, Fourier transforms.
Introduce the topics of probability, statistics, and random variables. The emphasis is on applications of probability to engineering problems and the ability to formulate such problems within the framework of probability theory.
Engineering applications of probability theory. Problems on events, independence, random variables, probability distribution and density
functions, expectations, and characteristic functions. Dependence, correlation, and regression; multi-variate Gaussian distribution.
1. Introduction: Probability
Concept of probability and probability spaces
Elementary probability theory
Conditional probability and Bayes' theorem
2. Repeated Trials
3. Random Variables and Distribution
Discrete and continuous random variables (binomial, Poisson, Gaussian…)
Functions of random variables
Joint and marginal distributions
Mean, variance and covariance
Conditional distribution and conditional expectation
Least squares estimation for Gaussian random vectors
5. Limit theorems
Laws of large numbers
Central limit theorem
A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill Press, 3rdEd, 1991.
Jay L. Devore,Probability and Statistics for Engineering and the Sciences，高等教育出版社，2004;