Goals and objectives  Course Outcomes  

1.  Students will be able to learn fundamental notions of probability such as probability distributions, conditional probability, law of large numbers. 
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2.  Students will be able to compute probability of events, expectation, variance, covariance, and correlations involving discrete and continuous random variables. 
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3.  Students will be able to use bootstrapping, maximum likelihood, and least square estimators. 
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4.  Students will be able to learn exploratory data analysis, samplesize selection for statistical inference, and methods of hypothesis testing as well as their limitations. 
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Class schedule  HW assignments (Including preparation and review of the class.)  Amount of Time Required  

1.  Discussion on applications of probability and statistics; Outcomes, events, and probability  Review Chapters 1 and 2 in the textbook  190分 
2.  Independence; Conditional probability; Bayes’ rule  Review Chapter 3 in the textbook (Homework assignment)  190分 
3.  Discrete random variables; Probability distributions; Probability mass functions; Discreteuniform, binomial distributions 
Review Chapter 4 in the textbook  190分 
4.  Continuous random variables; Cumulative distribution and probability density functions; Uniform, exponential, pareto, and normal distributions 
Review Chapter 5 in the textbook (Homework assignment)  190分 
5.  Expectation and variance; Simulation and computation with random variables  Review Chapter 7, Sections 6.2, 8.1, 8.2 in the textbook  190分 
6.  Joint distributions; Covariance and correlation  Review Chapters 9 and 10 in the textbook (Homework assignment)  190分 
7.  Law of large numbers, central limit theorem, and some of their applications  Review Sections 13.113.3, 14.1, 14.2 in the textbook  190分 
8.  Exploratory data analysis; Sampling; empirical distribution; Basic statistical models  Review Sections 15.3, 16.116.4, 17.117.4 in the textbook (Homework assignment)  190分 
9.  Bootstrap methods; Estimates and estimators  Review Sections 18.1, 18.2, Chapter 19 in the textbook  190分 
10.  Maximum likelihood and least square estimators  Review Chapters 21 and 22 in the textbook (Homework assignment)  190分 
11.  Confidence intervals; Choice of sample size  Review Chapter 24 in the textbook  190分 
12.  Hypotheses testing; PValues; Type I and Type II errors; ttest  Review Sections 25.125.3, 27.1,27.2 (Homework assignment)  190分 
13.  Discussions on applications of statistical methods  Review Sections 28.128.4  190分 
14.  Final exam and discussions on the solutions afterwards  Preparation for final  190分 
Total.      2660分 
Homework  Final  Total.  

1.  15%  15%  30% 
2.  15%  5%  20% 
3.  15%  5%  20% 
4.  15%  15%  30% 
Total.  60%  40%   
Work experience  Work experience and relevance to the course content if applicable 

N/A  N/A 