- The continuous random variable \(X\) has cumulative distribution function given by
$$\mathrm { F } ( x ) = \left\{ \begin{array} { c r }
0 & x < 1
1.5 x - 0.25 x ^ { 2 } - 1.25 & 1 \leqslant x \leqslant 3
1 & x > 3
\end{array} \right.$$
- Find the exact value of the median of \(X\)
- Find \(\mathrm { P } ( X < 1.6 \mid X > 1.2 )\)
The random variable \(Y = \frac { 1 } { X }\)
- Specify fully the cumulative distribution function of \(Y\)
- Hence or otherwise find the mode of \(Y\)