# Probability

> ML Prep practice set.

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

Move from events and conditioning through moments, distributions, and asymptotic results.

## Instructions

1. Name conditioning events and random variables explicitly.
2. Check independence before factorizing.

## Ordered items

1. [Counting, total probability, and independence](https://mlprep.iwase.dev/item/original-prob-foundations/?set=probability) — `original-prob-foundations` (easy, 7 min)
2. [Bayes rule and diagnostic evidence](https://mlprep.iwase.dev/item/pml-book1-ex2.9/?set=probability) — `pml-book1-ex2.9` (medium, 12 min)
3. [Events, unions, and conditional probability](https://mlprep.iwase.dev/item/mit-18-05-s2022-exam1-q1b/?set=probability) — `mit-18-05-s2022-exam1-q1b` (medium, 6 min)
4. [Joint tables, Bayes rule, and independence](https://mlprep.iwase.dev/item/mit-18-05-s2022-exam1-q3/?set=probability) — `mit-18-05-s2022-exam1-q3` (medium, 14 min)
5. [Recognize distribution moments](https://mlprep.iwase.dev/item/original-prob-distributions/?set=probability) — `original-prob-distributions` (easy, 8 min)
6. [Lognormal transformation by the CDF method](https://mlprep.iwase.dev/item/harvard-stat110-f2011-sp5-continuous-q1/?set=probability) — `harvard-stat110-f2011-sp5-continuous-q1` (medium, 12 min)
7. [Diagnostic testing with base rates](https://mlprep.iwase.dev/item/mit-18-05-s2022-exam1-q4/?set=probability) — `mit-18-05-s2022-exam1-q4` (medium, 8 min)
8. [Conditional expectation and total variance](https://mlprep.iwase.dev/item/original-prob-total-variance/?set=probability) — `original-prob-total-variance` (medium, 8 min)
9. [Linear transform of a multivariate Gaussian](https://mlprep.iwase.dev/item/original-prob-gaussian/?set=probability) — `original-prob-gaussian` (medium, 8 min)
10. [Joint density, moments, covariance, and correlation](https://mlprep.iwase.dev/item/mit-18-05-s2022-exam1-q5/?set=probability) — `mit-18-05-s2022-exam1-q5` (hard, 24 min)
11. [Central limit theorem for an aggregate](https://mlprep.iwase.dev/item/mit-18-05-s2022-exam1-q6/?set=probability) — `mit-18-05-s2022-exam1-q6` (medium, 10 min)
12. [LLN versus CLT](https://mlprep.iwase.dev/item/original-prob-lln/?set=probability) — `original-prob-lln` (easy, 5 min)

## Completion

Move fluently among event, distribution, expectation, and covariance representations.

## Next recommended practice

- [Statistics](https://mlprep.iwase.dev/set/statistics.md)