The continuous random variable \(X\) takes values in the interval \(0 \leqslant x \leqslant 5\) only. For \(0 \leqslant x \leqslant 5\) the graph of its probability density function f consists of two straight line segments, as shown in the diagram. Find \(k\) and show that f is given by $$f ( x ) = \begin{cases} \frac { 1 } { 8 } x & 0 \leqslant x \leqslant 2
\frac { 1 } { 4 } & 2 < x \leqslant 5
0 & \text { otherwise } \end{cases}$$ The random variable \(Y\) is given by \(Y = X ^ { 2 }\).

1. Find the probability density function of \(Y\).
2. Show that \(\mathrm { E } ( Y ) = 10.25\).
3. Show that the median of \(Y\) is the square of the median of \(X\).