本课程主要讲授以下内容: Introduction to Probability
Events, set theory and probability Basic relations of probability Conditional probability Bayes’s Theorem
2. Random Variables and Distributions Random variables and discrete distributions Continuous distributions Bivariate distributions and marginal distributions 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 |