# Statistics

> ML Prep practice set.

- Stable ID: `statistics`
- Area: mathematics
- Timebox: 130 minutes

Cover estimators, likelihood, Bayesian updating, intervals, tests, and simple regression.

## Instructions

1. Write the model before deriving an estimator or test.
2. Keep p-values and posterior probabilities distinct.

## Ordered items

1. [Bias, variance, MSE, and consistency](https://mlprep.iwase.dev/item/original-stats-estimator/?set=statistics) — `original-stats-estimator` (easy, 7 min)
2. [Maximum likelihood estimation from a density](https://mlprep.iwase.dev/item/mit-18-05-s2022-exam2-ii1/?set=statistics) — `mit-18-05-s2022-exam2-ii1` (medium, 12 min)
3. [Bayesian posterior density and normalization](https://mlprep.iwase.dev/item/mit-18-05-s2022-exam2-ii2/?set=statistics) — `mit-18-05-s2022-exam2-ii2` (hard, 15 min)
4. [Method of moments and Bayesian updating](https://mlprep.iwase.dev/item/original-stats-mom-map/?set=statistics) — `original-stats-mom-map` (medium, 10 min)
5. [One-sided test, critical value, and p-value](https://mlprep.iwase.dev/item/mit-18-05-s2022-exam2-ii4/?set=statistics) — `mit-18-05-s2022-exam2-ii4` (medium, 12 min)
6. [Confidence intervals with known and unknown variance](https://mlprep.iwase.dev/item/mit-18-05-s2022-pset11-q1/?set=statistics) — `mit-18-05-s2022-pset11-q1` (easy, 14 min)
7. [Chi-square test for a contingency table](https://mlprep.iwase.dev/item/mit-18-05-s2022-exam2-ii5/?set=statistics) — `mit-18-05-s2022-exam2-ii5` (hard, 18 min)
8. [Simple linear regression from Gaussian maximum likelihood](https://mlprep.iwase.dev/item/mit-18-05-s2022-pset6-q2/?set=statistics) — `mit-18-05-s2022-pset6-q2` (medium, 25 min)
9. [Linear transformations and quadratic expectations](https://mlprep.iwase.dev/item/pml-book1-ex3.4/?set=statistics) — `pml-book1-ex3.4` (medium, 15 min)
10. [Type I error, Type II error, and power](https://mlprep.iwase.dev/item/mit-18-05-s2022-exam2-i2/?set=statistics) — `mit-18-05-s2022-exam2-i2` (medium, 5 min)

## Completion

Derive and interpret one estimator, interval, hypothesis test, and posterior update from first principles.