Tag: probability

• Relearning Mathematics: Three Languages for Reading AIReads the inside of an LLM in three languages: linear algebra (embeddings, low-rank approximation), calculus (gradient descent, learning rate) and probability (cross-entropy, Bayes).Computer ScienceSurvival Strategy in the AI EraUndergraduatelinear algebracalculusprobabilitymachine learningabstraction~23 min
• The Monty Hall Problem: Why Switching Doors Doubles Your Chance of WinningYou pick one of three doors and the host opens a goat door. Enumeration and Bayes' theorem both push the win probability from 1/3 to 2/3, and we go on to biased hosts and n doors.MathematicsMathematical ColumnsHigh school / generalprobabilityconditional probabilityBayes theoremcounterintuitive results~28 min
• Probability Spaces and Kolmogorov's Axioms: Probability as a Measure of Total Mass OneFrom Bertrand's paradox to Kolmogorov's three axioms: sample spaces, σ-algebras, probability measures, and the continuity, Bayes and Borel–Cantelli results derived from them.MathematicsProbability TheoryUndergraduateprobabilitymeasure theorysigma-algebraBayes' theoremindependence~31 min