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