masszafüggvény

The term "masszafüggvény" is a Hungarian word that translates directly to "mass function." In the context of mathematics and statistics, it most commonly refers to a probability mass function (PMF). A probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value.

A probability mass function, denoted as $P(X=x)$, is defined for a discrete random variable $X$. This means $X$ can only take on a finite number of values or a countably infinite number of values. The function assigns a probability to each possible value of $X$. For any value $x$ that the random variable can take, the probability mass function $P(X=x)$ will be greater than or equal to zero. Furthermore, the sum of the probabilities for all possible values of $X$ must equal one.

Mathematically, a function $f(x)$ is a probability mass function of a discrete random variable $X$ if it satisfies two conditions: 1) $f(x) \geq 0$ for all possible values $x$, and 2) $\sum_{x} f(x) = 1$, where the sum is taken over all possible values of $X$. Examples of discrete random variables for which a PMF is used include the number of heads in a series of coin flips or the number of defective items in a sample. The concept is fundamental to understanding discrete probability distributions like the Bernoulli, binomial, and Poisson distributions.