开课单位:

数学科学研究所

课程代码:

MATH1212

课程名称:

概率论与数理统计I

英文名称:

Probability   and Statistics I

学分:

4

学时:

64

授课对象:

授课语言:

中英文

先修课程:

高等数学II

本课程的目的是使学生掌握概率论与数理统计的基本概念、基本理论与方法，为后续相关专业课程奠定必要的数学基础。

本课程主要讲授以下内容:

1. Introduction to Probability

1. Events, set theory and probability

2. Basic relations of probability

3. Conditional probability

4. Bayes’s Theorem

2.   Random   Variables and Distributions

1. Random variables and discrete distributions

2. Continuous distributions

3. Bivariate distributions and marginal distributions

4. Functions of random variables

3.  Expectation

a.  The expectation and   conditional expectation

b.  Variance and   moments

c.  Covariance and   correlation

d.  Generating   functions 

4.  Special   Distributions

a.  The Bernoulli and   binomial distributions

b.  The geometric   distributions

c.  The normal   distributions and the multi normal distributions

d.  The Poisson distribution   and the exponential distribution

5.  Large   Random Samples

a.  The law of large   numbers

b.  The central limit   theorem

6.  Estimations

a.  Parameter   estimation

b.  Interval estimation

7.  Hypothesis   Testing

a.  Significance level

b.  The t-test

c.  The F-distributions

8.  Linear   Statistical Models (optional)

a.  The method of least   square

b.  Linear regression

c.  Multiple regression

d.  Analysis of   variance