SES #  TOPICS 

Probability distributions and random variables 

I. Probability  
1  Sets and events (PDF) 
2  Probabilities and counting rules (PDF) 
3  Conditional probability and independence (PDF) 
II. Random variables and distribution functions  
4  Bayes theorem and random variables (PDF) 
5  Discrete and continuous random variables (PDF) 
6  Probability distribution functions (PDFs), cumulative distribution functions (CDFs), joint distribution of 2 or more random variables (PDF) 
7  Joint and marginal distributions (PDF) 
8  Review (PDF) 
Expectations and transformations of random variables 

III. Transformations of random variables  
9  Functions of random variables (PDF) 
10  Functions of several random variables (PDF 1) (PDF 2) 
IV. Expectations and conditional distributions  
11  Order statistics and expectations (PDF) 
12  Median, quantiles, and variance (PDF) 
13  Covariance and conditional expectations (PDF) 
V. Special distributions  
14  Conditional expectations and special distributions (PDF) 
VI. Law of large numbers and central limit theorems  
15  Law of large numbers (PDF) 
16  Review (PDF) 
Estimation and hypothesis tests 

VII. Estimation methods and properties  
17  Central limit theorem, estimators, bias, and consistency (PDF) 
18  Constructing estimators (PDF) 
VIII. Confidence intervals  
19  Confidence intervals (PDF) 
20  Confidence intervals (cont.) (PDF) 
IX. Hypothesis testing  
21  Hypothesis tests (PDF) 
22  Hypothesis tests (cont.) (PDF) 
23  Hypothesis tests (cont.) (PDF) 
24  Review (PDF) 
Lecture Notes
Course Info
Learning Resource Types
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Exams
notes
Lecture Notes
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Problem Sets with Solutions