7 The probability density function of the random variable \(X\) is given by
$$f ( x ) = \begin{cases} \frac { 3 } { 4 } x ( c - x ) & 0 \leqslant x \leqslant c
0 & \text { otherwise } \end{cases}$$
where \(c\) is a constant.
- Show that \(c = 2\).
- Sketch the graph of \(y = \mathrm { f } ( x )\) and state the median of \(X\).
- Find \(\mathrm { P } ( X < 1.5 )\).
- Hence write down the value of \(\mathrm { P } ( 0.5 < X < 1 )\).