Grad-level Probability and Statistics Lecture Notes

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Below you will find lecture notes for a graduate level probability and statistics course. The notes are written to maximize understanding.

Probability Lectures

- Lecture 1: Probability Theory, Probability Space, Random Variables, Cumulative Distribution Function
  (section-by-section | single page)
 
- Lecture 2: Random Variables, Leibniz Rule and Transformations of RVs
  (section-by-section | single page)
 
- Lecture 3: Expectations of RVs and Moments
  (section-by-section | single page)
 
- Lecture 4: Examples of Distributions
  (section-by-section | single page)

- Lecture 5: Families of Distributions, Chebychev's Inequality, Multiple Random Variables
  (section-by-section | single page)

- Lecture 6: Multiple RVs (cont.), Conditional Moments, LIE, CVI, Covariance and Correlation, Some Inequalities
  (section-by-section | single page)

Statistics Lectures

- Lecture 7: Random Sample, Statistics, Statistical Inference
  (section-by-section | single page)

- Lecture 8: Point Estimation, Method of Moments, Maximum Likelihood
  (section-by-section | single page)
- Lecture 9: Point Estimation (cont.), Evaluating Estimators, UMVU, Sufficient Statistics, Rao-Blackwell
  (section-by-section | single page)
- Lecture 10: Finding UMVU Estimators, Complete Statistics, Cramér-Rao Lower Bound 
  (section-by-section | single page)