Probability as bookkeeping
Probability is careful accounting for what you don't know. Sample spaces, distributions, Bayes' rule as a picture, expectation and covariance, the Gaussian in one and many dimensions, and the two limit theorems stated correctly.
55 min
After this lesson you can
- Define sample spaces, events, random variables, pmfs and pdfs, and say why a density can exceed 1
- Move between joint, marginal and conditional distributions with the sum and product rules
- Derive Bayes' rule and apply it to a base-rate problem
- Compute expectations, variances and covariances, and read a covariance matrix as an ellipse
- State the law of large numbers and the central limit theorem with their conditions
In this lesson
- Outcomes, events and the rules of the game
- Random variables and their distributions
- Joint, marginal and conditional
- Bayes’ rule, as a picture
- Expectation, variance, covariance
- The Gaussian
- Two limit theorems, stated carefully
- In code
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