jaotuvusfunktsiooni

Jaotuvusfunktsioon, known in English as the distribution function, is a fundamental concept in probability theory and statistics. It describes the probability that a random variable will take on a value less than or equal to a specific point. Formally, for a random variable X, the distribution function is denoted by F(x) and is defined as F(x) = P(X ≤ x), where P denotes probability.

The distribution function is a non-decreasing function. This means that if a is less than or equal to b, then F(a) must be less than or equal to F(b). It also has specific limits: as x approaches negative infinity, the distribution function approaches 0, and as x approaches positive infinity, it approaches 1. These properties ensure that the probabilities are consistently represented.

There are two main types of distribution functions corresponding to the types of random variables: cumulative distribution functions (CDFs) for continuous random variables and probability mass functions (PMFs) for discrete random variables. For continuous variables, the CDF is used, while for discrete variables, the PMF describes the probability of each specific outcome. The distribution function is crucial for understanding the behavior and characteristics of random phenomena, aiding in modeling, analysis, and prediction across various scientific and engineering disciplines.