a) The diagrams show the graphs of two functions, g and h. For each of the functions g and h, give a reason why it cannot be a probability density function.

b) The distance, in kilometres, travelled in a given time by a cyclist is represented by the continuous random variable $X$ with probability density function given by

$f\left( x \right) = \left\{ \begin{gathered}
  \frac{{30}}{{{x^2}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10 \leqslant x \leqslant 15, \hfill \\
  0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,otherwise. \hfill \\ 
\end{gathered}  \right.$

(i) Show that $E\left( X \right) = 30{\text{ }}ln{\text{ }}1.5.$

(ii) Find the median of $X$. Find also the probability that $X$ lies between the median and the mean.