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週次 |
日期 |
單元主題 |
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第1週 |
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Introduction
(1) What is statistics?
(2) Probability and probability model
Exploratory data analysis
(1) Sample statistics (mean, variance, median, mode, quantiles)
(2) Histogram and box-and-whisker plot
(3) Empirical cumulative distribution function |
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第2週 |
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Random variable and probability distribution
(1) Definition of random variable
(2) Discrete and continuous random variables
(3) Cumulative distribution function and probability density function |
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第3週 |
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Characterizing a random variable
(1) Expectation, variance, and quantile
(2) Moments and moment generating function
(3) Expectation of a function of a random variable |
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第4週 |
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Univariate distributions (I) Discrete distributions
(1) Uniform distribution
(2) Bernoulli distribution
(3) Binomial distribution
(4) Negative binomial distribution
(5) Geometric distribution
(6) Poisson distribution |
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第5週 |
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Univariate distributions (II) Continuous distribution
(1) Uniform or rectangular distribution
(2) Normal distribution
(3) Exponential distribution
(4) Gamma distribution
(5) Pearson Type III distribution
(6) Log normal and log Pearson Type III distributions |
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第6週 |
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調整放假 |
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第7週 |
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Joint distribution and conditional distribution
(1) Joint cumulative distribution function and joint probability density function
(2) Marginal density function
(3) Conditional distribution and conditional density function
(4) Covariance and correlation
(5) Bivariate normal distribution |
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第8週 |
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期中考 |
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第9週 |
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Sampling and sampling distributions (I)
(1) Definition of random sample
(2) Definition of a statistic
(3) Sample moments
(4) The Central Limit Theorem |
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第10週 |
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Sampling and sampling distributions (II)
(1) Student's t distribution
(2) Chi-square distribution
(3) F distribution
(4) Order statistics |
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第11週 |
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Statistical inference (I) Parameter point estimation
(1) Estimators and estimates
(2) Method of moments
(3) Maximum likelihood method
(4) Properties of estimators |
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第12週 |
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Statistical inference (II) Parameter interval estimation (1) Confidence interval for the mean (2) Confidence interval for the variance (3) Confidence Interval for Difference in Means (4) Confidence interval for a population proportion, p |
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第13週 |
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Hypothesis tests (I)
(1) Null and alternative hypothese
(2) The Critical Region and Test Statistics
(3) The Power Function
(4) Types of error |
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第14週 |
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Hypothesis tests (II) One-sample tests on the mean and
variance
(1) Tests on Mean
(2) Tests on Variance
(3) Paired t-test |
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第15週 |
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Hypothesis tests (III) Nonparametric Goodness-of-fit (GOF) tests
(1) Goodness-of-fit test
(2) Chi-square GOF test
(3) Kolmogorov-Smirnov GOF test |
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第16週 |
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Linear Regression (I)
(1) The Method of Least Squares
(2) Coefficient of determination
(3) Estimating the variance of Y|x |
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第17週 |
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Linear Regression (II)
(4) Confidence intervals of the regression coefficients
(5) Hypothesis tests for regression coefficients
(6) Confidence interval of the regression estimate
(7) Prediction interval of the predicted value |
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第18週 |
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期末考 |