Probabilistikas

Probabilistikas, commonly translated as probability theory, is a branch of mathematics that studies randomness and the quantification of uncertainty. It provides formal rules for modeling uncertain events and drawing conclusions from incomplete information. A central concept is the probability space (Ω, F, P), which consists of a set of outcomes, a σ-algebra of events, and a probability measure assigning weights to events. Random variables map outcomes to numerical values; their distributions describe how likely different values are. Core tools include expectation, variance, and covariation, as well as notions of independence and conditional probability. Fundamental results include the Law of Large Numbers and the Central Limit Theorem, which describe long-run behavior of sums of random variables.

Fields within probabilistikas include discrete and continuous probability, stochastic processes (such as Markov chains, Poisson processes, Brownian motion), and Bayesian probability, which treats probability as a degree of belief updated by data. The axiomatic foundation was established by Andrey Kolmogorov in 1933, providing rigorous underpinnings for measure-theoretic probability; earlier work by Jacob Bernoulli, Pierre-Simon Laplace and others shaped its development.

Applications span statistics, finance, physics, engineering, computer science, and risk assessment. Computational methods, such as Monte Carlo simulation and Bayesian computation, enable practical analysis of complex models. The field continues to interact with data science, machine learning, and quantitative research, forming a core toolkit for modeling uncertainty in real-world systems.