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

Suppose that a continuous random variable has the probability density function

where is a constant. Find the value of .

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Suppose that a continuous random variable $X$ has the probability density function

$f(x)=\left\{{\begin{array}{ll}ax^{2}&{\mbox{if }}2\leq x\leq 3\\&\\{\frac {12}{31}}&{\mbox{if }}1\leq x<2\end{array}}\right.$

where $a$ is a constant. Find the value of $a$.