7 The continuous random variable \(X\) has a cumulative distribution function \(\mathrm { F } ( x )\), where
$$\mathrm { F } ( x ) = \left\{ \begin{array} { l r }
0 & x < 1
\frac { 1 } { 4 } ( x - 1 ) & 1 \leqslant x < 4
\frac { 1 } { 16 } \left( 12 x - x ^ { 2 } - 20 \right) & 4 \leqslant x \leqslant 6
1 & x > 6
\end{array} \right.$$
- Sketch the probability density function, \(\mathrm { f } ( x )\), on the grid below.
- Find the mean value of \(X\).