Probability distributions and random variables

I. Probability
1 Sets and events  
2 Probabilities and counting rules  
3 Conditional probability and independence  
II. Random variables and distribution functions
4 Bayes theorem and random variables Problem set 1 due
5 Discrete and continuous random variables  
6 Probability distribution functions (PDFs), cumulative distribution functions (CDFs), joint distribution of 2 or more random variables Problem set 2 due
7 Joint and marginal distributions  
8 Review Problem set 3 due
E1 Exam 1  

Expectations and transformations of random variables

III. Transformations of random variables
9 Functions of random variables  
10 Functions of several random variables Problem set 4 due
IV. Expectations and conditional distributions
11 Order statistics and expectations  
12 Median, quantiles, and variance  
13 Covariance and conditional expectations  
V. Special distributions
14 Conditional expectations and special distributions Problem set 5 due
VI. Law of large numbers and central limit theorems
15 Law of large numbers  
16 Review Problem set 6 due
E2 Exam 2  

Estimation and hypothesis tests

VII. Estimation methods and properties
17 Central limit theorem, estimators, bias, and consistency  
18 Constructing estimators Problem set 7 due
VIII. Confidence intervals
19 Confidence intervals  
20 Confidence intervals (cont.) Problem set 8 due
IX. Hypothesis testing
21 Hypothesis tests  
22 Hypothesis tests (cont.)  
23 Hypothesis tests (cont.) Problem set 9 due
24 Review  
E3 Exam 3