# 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)
```