- The continuous random variable \(X\) has cumulative distribution function given by
$$\mathrm { F } ( x ) = \left\{ \begin{array} { c r }
0 & x < 2
1.25 - \frac { 2.5 } { x } & 2 \leqslant x \leqslant 10
1 & x > 10
\end{array} \right.$$
- Find \(\mathrm { P } ( \{ X < 5 \} \cup \{ X > 8 \} )\)
- Find the median of \(X\).
- Find \(\mathrm { E } \left( X ^ { 2 } \right)\)
- Sketch the probability density function of \(X\).
- Describe the skewness of the distribution of \(X\).