# Probability Practice

> ML preparation set.

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

## Completion

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