Suppose that a continuous random variable X {\displaystyle X} has the probability density function
f ( x ) = { a x 2 if 2 ≤ x ≤ 3 12 31 if 1 ≤ x < 2 {\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 a {\displaystyle a} is a constant. Find the value of a {\displaystyle a} .
