# Science:Math Exam Resources/Courses/MATH105/April 2016/Question 04 (a)/Statement

Suppose that a continuous random variable ${\displaystyle X}$ has the probability density function
${\displaystyle f(x)=\left\{{\begin{array}{ll}ax^{2}&{\mbox{if }}2\leq x\leq 3\\&\\{\frac {12}{31}}&{\mbox{if }}1\leq x<2\end{array}}\right.}$
where ${\displaystyle a}$ is a constant. Find the value of ${\displaystyle a}$.