The continuous random variable \(X\) has probability density function f given by \(f(x)=\left\{\begin{array}{ll} \frac{4}{9}(x+1) & 0 \leqslant x \leqslant 1 \\ (x-2)^{2} & 1\lt x \leqslant 2 \\ 0 & \text { otherwise } \end{array}\right.\) (a) Find the cumulative distribution function of \(X\). (b) Find the exact value of the median of \(X\). The random variable \(Y\) is defined by \(Y=\sqrt{X}\). (c) Find the cumulative distribution function of \(Y\). (d) Determine whether the median of \(Y\) is greater than, or less than, the median of \(X\).