Probability distributions over finite outcomes provide the mathematical framework for modeling uncertainty in systems where a random variable can take on values from a discrete, countable set. The core principle defines a function mapping each possible outcome to its associated probability measure, ensuring that the sum of all probabilities equals one and every individual value is non-negative. This concept serves as a foundational element within classical statistics and information theory, establishing necessary bounds for entropy calculations and expectation values required in algorithmic runtime analysis.
Introduces probability distributions: random variables, discrete distributions over countable outcomes versus continuous densities, and the common families used to model data.