A continuous random variable \(X\) has probability density function f given by \(f(x)=\left\{\begin{array}{ll} \frac{1}{16} \sqrt{x} & 0 \leqslant x\lt 4 \\ \frac{1}{k \sqrt{x}} & 4 \leqslant x \leqslant 9 \\ 0 & \text { otherwise } \end{array}\right.\) where \(k\) is a constant. (a) Show that \(k=3\). (b) Find the median value of \(X\). The random variable \(Y\) is defined by \(Y=\sqrt{X}\). (c) Find the probability density function of \(Y\).