The mathematical description of a random variable in terms of its admissible values and the probability associated, in an appropriate sense, with each value. The probability distribution of a continuous variate is defined by stating the mathematical equation of the distribution function F(x) or the probability density function f(x) (if it exists) together with the range over which the equation holds. The probability distribution of a discrete variate is commonly defined by stating the equation for the probability p(x) that the variate will assume any particular value x, and indicating what values are possible.