統計學 STATISTICS
台灣大學生物環境系統工程學系 授課教師：鄭克聲教授
課號：602 23900 學分數：3
Office: 生工系Room 109, E-mail: rslab@ntu.edu.tw

Syllabus
1.Introduction
What is statistics?
Deterministic vs. stochastic
2.Definition of Probability
a priori probability
a posteriori probability
probability model
3.Random Variables and Probability Distributions
Discrete random variables
Continuous random variables
4.Joint and Conditional Distributions
Joint distribution functions
Conditional distributions and stochastic independence
Expectation and covariance
Bivariate Normal distribution
5.Distributions of Functions of Random Variables
Expectations of functions of random variables
CDF Technique
Moment-generating-function technique
The transformation technique
6.Sampling Distributions and Descriptive Statistics
Populations and random samples
Statistic and sample moments
Weak law of large numbers
Central-limit theorem
Distributions of sample means
Sampling from the normal distribution
Order statistics
7.Parameter Estimation – Point Estimation
Method of moments
Maximum likelihood method
8.Parameter Estimation – Interval Estimation
Confidence intervals
Methods of finding CIs
- Pivotal quantity method
- Statistical method
Parameter CIs for Samps from the normal distribution
9.Test of Hypotheses
Definition of test of a statistical hypothesis
Definition of power function
Hypothesis test on the mean
Hypothesis test on the variance
Hypothesis test on confidence intervals
Chi-square goodness-of-fit test
10.Linear Models
Description of linear models
Least-squares estimation
Properties of LSE
Confidence intervals of estimators of model parameters
Hypothesis test on parameter estimators
Residual Analysis

Grading:
Three sxams: 20%, 20%, 30%
Homeworks: 30% (5%@6)
Grades may be adjusted depending on class attendance of individuals.

Textbook:
Milton, J.S. and Arnold, J.C., 2003. Introduction to Probability and Statistics. McGraw-Hill Co., 4th edition.