- The continuous random variable \(Y\) has cumulative distribution function \(\mathrm { F } ( y )\) given by
$$\mathrm { F } ( y ) = \left\{ \begin{array} { c l }
0 & y < 1
k \left( y ^ { 4 } + y ^ { 2 } - 2 \right) & 1 \leqslant y \leqslant 2
1 & y > 2
\end{array} \right.$$
- Show that \(k = \frac { 1 } { 18 }\).
- Find \(\mathrm { P } ( Y > 1.5 )\).
- Specify fully the probability density function f(y).