Lecture Notes


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)