Probability and Statistics

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Syllabus

SYLLABUS of Probability and Statistics

Credits: 48credit hours.

Class Meetings: 16sessions / week

                            3hours / session

 


Prerequisites

Knowledge of basic matrix analysis, continuous and discrete time signal and systems analysis, Fourier transforms.

 

Objective:

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.

 

Description:

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.

 

Content:

1. Introduction: Probability

Concept of probability and probability spaces

Elementary probability theory

Conditional probability and Bayes' theorem

2. Repeated Trials

Combined experiments

Bernoulli trials

Poisson theorem

3. Random Variables and Distribution

Discrete and continuous random variables (binomial, Poisson, Gaussian…)

Functions of random variables

Joint and marginal distributions

Independence

4. Expectation

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

6. Statistics

Parameter estimation

Hypothesis testing

 

Text:

A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill Press, 3rdEd, 1991.

 

Reference book:
Jay L. Devore,Probability and Statistics for Engineering and the Sciences,高等教育出版社,2004;