In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values.

For a more precise definition one needs to distinguish between discrete and continuous random variables. In the discrete case, one can easily assign a probability to each possible value: when throwing a die, each of the six values 1 to 6 has the probability 1/6. In contrast, when a random variable takes values from a continuum, probabilities are nonzero only if they refer to finite intervals: in quality control one might demand that the probability of a "500 g" package containing between 490 g and 510 g should be no less than 98%.

If a total order is defined for the random variable, the cumulative distribution function gives the probability that the random variable is no larger than a given value; it is the integral of the non-cumulative distribution.

As probability theory is used in quite diverse applications, terminology is not uniform and sometimes confusing. The following terms are used for non-cumulative probability distribution functions: