# Probability mass function

A random experiment with finite or countably infinite number of possible outputs can be described by a probability function (English: probability function or probability mass function) describe which indicates the occurrence probability for each outcome of the experiment. In the mathematical branch stochastic random experiments are modeled by random variables, the random (numeric ) value is interpreted as the expression of a given random feature and inscribed.

The probability function is then applied to the occurrence probabilities of the individual characteristics of the modeled characteristic of a discrete random variable.

It is the counterpart of the density function for continuous random variables and is therefore also referred to as a probability density.

The cumulative distribution function of the probability densities by summation.

## Probability function

A discrete random variable takes a finite or countably infinitely many values . Each of these values can be assigned a probability with which the random variable takes this value ( with which they " occurs with this expression of the characteristic ").

The probability distribution is then given by

Given.

The sum of the probabilities must be 1 result that corresponds to the requirement that all possible values have been considered.

The likelihood function is the density of maßtheoretischer view with respect to the distribution of Zählmaßes to the set of possible values .

## Distribution function

The (cumulative ) distribution function is calculated by summing the values of the likelihood function to

The sum of all forms of running, or are less than or equal.

### Example

The random variable is the result of the dice. The distribution of the probability function is given by

- The probability of throwing a six is
- The probability of rolling a maximum of three, can be deduced from the distribution function:

- Random variable
- Probability distribution
- Stochastics