The cumulative distribution function of a random variable is the chance that the random variable is less than or equal to x, as a function of x. In symbols, if F is the cdf of the random variable X, then F(x) = P( X ≤ x). The cumulative distribution function must tend to zero as x approaches minus infinity, and must tend to unity as x approaches infinity. It is a positive function, and increases monotonically: if y > x, then F(y) ≥ F(x). The cumulative distribution function completely characterizes the probability distribution of a random variable.