ai-tutorialsbasicsprobability-theory
Probability Theory Explained: Sample Spaces, Random Variables, and the Expectation You Already Optimise
Probability for practitioners who need it for machine learning: why a probability is a function on questions rather than a property of things, why a density can be 40 and is still not a probability, why expectation is linear whether or not anything is independent, why the conditional mean is the best predictor by theorem rather than by training, why cross-entropy's minimiser is calibrated for the same reason, and the seven places — a density mistaken for a probability, base rates, Simpson's paradox, uncorrelated-but-dependent, infinite means, conditioning on a zero-probability event, and 'random' without a measure — where the intuition breaks and the definition does not.
Oct 29, 2026•47 min read
