Graduate Level: Intro to Probability and Statistics

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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)