Continuous random variable

A random variable whose cumulative distribution function is continuous, equivalently whose probability distribution assigns zero probability to every singleton. In elementary applications, one usually additionally assumes a probability density function; that stronger property means its law is an absolutely continuous probability distribution. A continuous cumulative distribution function alone need not admit a probability density function.

A random variable with a probability density function $f$, so its cumulative distribution function is $F(x)={\int }_{-\infty }^{x}f(t)dt$. Equivalently, its law is an absolutely continuous probability distribution. In particular, the probability of every singleton is zero.