continuous random variable

A continuous variable subject to random variation. The probability distribution is defined by the probability density function. It is usual also to require that, for each real number x, P(X=x)=0. As a result it is immaterial whether '<' or '≤' is used in probability statements, since e.g. P(X≤x)=P(X<x) and P(x₁≤X≤x₂)=P(x₁<X<x₂).