Probabilistyka

Probabilistyka, in English often translated as the theory of probability, is a branch of mathematics that studies random phenomena, uncertainty, and the methods used to quantify and reason about them. It develops models based on random variables, probability distributions, and measures of uncertainty, and it investigates how these models behave under arithmetic operations, conditioning, and limiting processes. Core topics include expectation and variance, independence, joint and conditional distributions, limit theorems, and the foundations of mathematical statistics.

A major part of probabilistyka concerns stochastic processes, which describe systems evolving over time under uncertainty. This includes Markov processes and chains, martingales, Brownian motion, and other models used in finance, physics, and engineering. The field also encompasses statistical inference, estimation, hypothesis testing, and Bayesian methods, combining theoretical results with practical data analysis. Applications are widespread and include finance, risk assessment, queueing theory, reliability, economics, biology, computer science, and data science.

Historically, probabilistyka emerged from problems in games of chance posed by early mathematicians and was formalized in the 20th century through axiomatic foundations, notably by Andrey Kolmogorov. In Poland and other countries, probabilistyka is taught as a core part of mathematics and statistics curricula, with both theoretical research and applied work addressing interdisciplinary problems.

See also: probability theory, mathematical statistics, stochastic processes, random variable.