tömegfüggvénye

A tömegfüggvénye, often translated as mass function or probability mass function (PMF), is a function that describes the probability distribution of a discrete random variable. For a discrete random variable X, the probability mass function P(X=x) gives the probability that X takes on the exact value x. The possible values for x are typically integers or a finite set of values. The sum of the probabilities for all possible values of a discrete random variable must equal 1, meaning that Σ P(X=x) = 1 for all possible x. The tömegfüggvénye is always non-negative, with P(X=x) ≥ 0 for all x. This concept is fundamental in probability theory and statistics for analyzing discrete data. It is used in various applications, including modeling the number of successes in a fixed number of trials (binomial distribution), the number of events occurring in a fixed interval (Poisson distribution), and the outcome of a single trial with two possibilities (Bernoulli distribution). Understanding the tömegfüggvénye allows for calculating expected values, variances, and probabilities of various events related to the random variable.