Probability

A measure of uncertainty over events, formalized as a function mapping outcomes to values in [0, 1].

• Axioms: Kolmogorov’s axioms ground probability in set theory and measure theory
• Bayes theorem inverts conditional probabilities, enabling inference from evidence
• distributions (normal, Poisson, exponential) characterize random variables
• stochastic processes (Markov chains, Brownian motion) model evolution over time
• law of large numbers and central limit theorem bridge probability to statistics
• entropy connects probability to information theory and thermodynamics
• Foundation of machine learning, game theory, quantum mechanics, and optimization
• Related: combinatorics, calculus, differential equations