Question: If the probability density function of \(X\) is

\[f(x)=\left\{ \begin{aligned} & \frac{c}{\sqrt{x}}\text{ for }0<x<4 \\ & \text{ }0\text{ elsewhere} \\ \end{aligned} \right.\]

(a) Determine the value of \(c\).

(b) Find \(\Pr \left( X<\frac{1}{4} \right)\).

(c) Find \(\Pr (X>1)\).