2. The continuous random variable \(Y\) has cumulative distribution function
$$\mathrm { F } ( y ) = \left\{ \begin{array} { c c }
0 & y < 0
\frac { 1 } { 4 } \left( y ^ { 3 } - 4 y ^ { 2 } + k y \right) & 0 \leqslant y \leqslant 2
1 & y > 2
\end{array} \right.$$
where \(k\) is a constant.
- Find the value of \(k\).
- Find the probability density function of \(Y\), specifying it for all values of \(y\).
- Find \(\mathrm { P } ( Y > 1 )\).