5. The continuous random variable \(Y\) has cumulative distribution function \(\mathrm { F } ( y )\) given by
$$\mathrm { F } ( y ) = \left\{ \begin{array} { l r }
0 & y < 3
k \left( y ^ { 2 } - 2 y - 3 \right) & 3 \leqslant y \leqslant \alpha
4 k ( 2 y - 7 ) & \alpha < y \leqslant 6
1 & y > 6
\end{array} \right.$$
where \(k\) and \(\alpha\) are constants.
- Find \(\mathrm { P } ( 4.5 < Y \leqslant 5.5 )\)
- Find the probability density function \(\mathrm { f } ( \mathrm { y } )\)