STATISTICS -- Fall, 2011
Syllabus
Professor Ke-Sheng Cheng
Office: Room 115, Building No. 5
Email: rslab@ntu.edu.tw
1.  Introduction   
(1)        What is statistics?
(2)        Deterministic vs. stochastic
(3)        Definition of Probability
  •        a priori probability
  •        a posteriori probability
  •        probability model
Homework-1 (HW1_Data, Class_ID)

2.  Random variables and probability distributions [updated 10/02/2011]
(1)        Definition of random variable
(2)        Cumulative distribution function (CDF) and Probability  density function (PDF)
(3)        Characterizing random variables
  •              Expectation
  •        Variance
  •        Moments
  •        Median
  •        Mode
  •        Quantiles
(4)        Moment generating function
(5)        Chebyshev inequality
Homework-2

3.  Discrete random variables
(1)        Discrete uniform distribution
(2)        Bernoulli distribution
(3)        Binomial distribution
(4)        Negative binomial distribution
(5)        Geometric distribution
(6)        Hypergeometric distribution
(7)        Poisson distribution     

4.  Continuous random variables
(1)        Uniform distribution
(2)        Normal distribution
(3)        Exponential distribution
(4)        Gamma distribution
(5)        Pearson type III distribution
(6)        Chi-square distribution
(7)        Approximations between random variables   
(8)        Transformation of random variables
(9)        Random number generation and stochastic simulation
Homework-3  HW3DATA.txt
*** The midterm exam is scheduled on Nov. 8 from 9:10 to 12:10 a.m. ***
5.  Joint and conditional distributions
(1)        Joint density function
(2)        Marginal density function
(3)        Conditional density function
(4)        Covariance and correlation coefficient
(5)        Bivariate normal distribution (BVN)
(6)        Simulation of BVN random samples
Homework-4  

6.  Sampling and sampling distributions  [Updated on Nov. 21, 2011]  
(1)        Random sample
(2)        Definition of statistic
(3)        Sample statistics
(4)        Weak law of large numbers
(5)        Central limit theorem
(6)        Sampling distributions
(7)        Order statistics


7.  Point estimation
(1)        Statistical inference
(2)        Estimator and estimate
(3)        Method of moments
(4)        Maximum likelihood estimator
(5)        Properties of point estimators
  • Unbiased estimator
  • Mean squared error of an estimator
Homework-5   HW5DATA.txt  (uploaded on Dec. 4, 2011)

8.  Interval estimation
(1)        Variation of sample statistics
(2)        Confidence interval as a random interval
(3)        Estimating confidence interval of the mean - an example
(4)        Pivotal quantity method for confidence interval estimation
(5)        Review of sampling distributions
(6)        Confidence interval for the mean
(7)        Confidence interval for the variance
(8)        Confidence interval for difference in means
(9)        Confidence interval for a population proportion
Homework-6

9.  Hypothesis test (PPT-1, PPT-2, PPT-3)  
(1)        What is hypothesis test?
(2)        Null and alternative hypotheses
(3)        Fundamental concepts of hypothesis test
(4)        Test statistics and the critical region
(5)        Types of error and the power function
(6)        One-sample tests on the mean and variance
(7)        Non-parametric goodness-of-fit tests
Homework-7; Chisq_Test.R  

10.        Linear models
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