Graduate Level: Intro to Probability and Statistics

Lecture Notes

01	Probability Theory, Probability Space, Random Variables, Cumulative Distribution Function (section-by-section | single page)

10	Finding UMVU Estimators, Complete Statistics, Cramér-Rao Lower Bound (section-by-section | single page)

02	Random Variables, Leibniz Rule and Transformations of RVs (section-by-section | single page)

11	Hypothesis Testing, Power Function, Selecting the Critical Value (section-by-section | single page)

03	Expectations of RVs and Moments (section-by-section | single page)

12	Hypothesis Testing (cont.), LRT, LM, Wald, Test Equivalence, Test Optimality (section-by-section | single page)

04	Examples of Distributions (section-by-section | single page)

13	Test Optimality (cont.), 2-sided tests, p-values, Interval Estimation (section-by-section | single page)

05	Families of Distributions, Chebychev's Inequality, Multiple Random Variables (section-by-section | single page)

14	Convergence, Law of Large Numbers, Central Limit Theorem, Delta Method (section-by-section | single page)

06	Multiple RVs (cont.), Conditional Moments, LIE, CVI, Covariance and Correlation, Some Inequalities (section-by-section | single page)

15	Asymptotic Properties of ML Estimators (section-by-section | single page)

07	Random Sample, Statistics, Statistical Inference (section-by-section | single page)

16	Bayesian Estimation (section-by-section | single page)

08	Point Estimation, Method of Moments, Maximum Likelihood (section-by-section | single page)

17	OLS, Normal Linear Model, Asymptotic Properties (section-by-section | single page)

09	Point Estimation (cont.), Evaluating Estimators, UMVU, Sufficient Statistics, Rao-Blackwell (section-by-section | single page)

18	Multicollinearity, Partitioned Regression, Gauss-Markov Theorem (section-by-section | single page)