- The continuous random variable \(X\) has probability density function \(\mathrm { f } ( x )\) given by
$$f ( x ) = \left\{ \begin{array} { c c }
2 ( x - 2 ) & 2 \leqslant x \leqslant 3
0 & \text { otherwise }
\end{array} \right.$$
- Sketch \(\mathrm { f } ( x )\) for all values of \(x\).
- Write down the mode of \(X\).
Find
- \(\mathrm { E } ( X )\),
- the median of \(X\).
- Comment on the skewness of this distribution. Give a reason for your answer.