2 The cumulative distribution function of the continuous random variable, \(Y\), is given below.
$$\mathrm { F } ( y ) = \left\{ \begin{array} { c c }
0 & y < 0
\frac { y ^ { 3 } - y ^ { 2 } } { 4 } & 1 \leq y \leq 2
1 & y > 2
\end{array} \right.$$
- Find \(\mathrm { P } ( Y \leq 1.5 )\)
- Verify that the median of \(Y\) lies between 1.6 and 1.7.
- Find the probability density function of \(Y\).