7. The continuous random variable \(X\) has probability density function \(\mathrm { f } ( x )\) given by $$\mathrm { f } ( x ) = \left\{ \begin{array} { c c } \frac { x ^ { 2 } } { 45 } & 0 \leqslant x \leqslant 3
\frac { 1 } { 5 } & 3 < x < 4
\frac { 1 } { 3 } - \frac { x } { 30 } & 4 \leqslant x \leqslant 10
0 & \text { otherwise } \end{array} . \right.$$

1. Sketch \(\mathrm { f } ( x )\) for \(0 \leqslant x \leqslant 10\)
2. Find the cumulative distribution function \(\mathrm { F } ( x )\) for all values of \(x\).
3. Find \(\mathrm { P } ( X \leqslant 8 )\).