Probabilitete

Probabilitete is a term used in several languages to denote probabilities or the study of probability. In mathematics, probabilitete refers to the likelihood of events and the framework for reasoning about uncertainty. Probability theory formalizes probability as a measure on a set of outcomes, typically represented by a probability space (Ω, F, P), where Ω is the set of possible outcomes, F is a sigma-algebra of events, and P assigns to each event a number between 0 and 1. The axioms require non-negativity, P(Ω)=1, and additivity over disjoint events. For any events A and B with P(B)>0, conditional probability P(A|B)=P(A∩B)/P(B). Independence if P(A∩B)=P(A)P(B). Random variables map outcomes to numbers; their expectation E[X] and variance Var(X) summarize central tendency and dispersion.

Discrete models assign probabilities to individual outcomes; continuous models use probability density functions and the cumulative distribution function F(x)=P(X≤x). Foundational theorems include the Law of Large Numbers and the Central Limit Theorem, describing behavior of sums of random variables. Applications span finance, science, engineering, and risk assessment, with methods ranging from frequentist estimation to Bayesian inference. Limitations include the fact that probabilities express uncertainty rather than certainties and depend on the chosen model and available data.