A random variable <math>X</math> has a continuous probability distribution if there is a function <math>f: \mathbb{R} \rightarrow [0, \infty)</math> such that for each interval <math>I \subset \mathbb{R}</math> the probability of <math>X</math> belonging to <math>I</math> is given by the integral of <math>f</math> over <math>I</math>.<ref>Chapter 3.2 of {{harvp|DeGroot, Morris H.|Schervish, Mark J.|2002}}</ref> For example, if <math>I = [a, b]</math> then we would have: | A random variable <math>X</math> has a continuous probability distribution if there is a function <math>f: \mathbb{R} \rightarrow [0, \infty)</math> such that for each interval <math>I \subset \mathbb{R}</math> the probability of <math>X</math> belonging to <math>I</math> is given by the integral of <math>f</math> over <math>I</math>.<ref>Chapter 3.2 of {{harvp|DeGroot, Morris H.|Schervish, Mark J.|2002}}</ref> For example, if <math>I = [a, b]</math> then we would have: |