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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.
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
$$f ( x ) = \begin{cases} \frac { 30 } { x ^ { 2 } } & 10 \leqslant x \leqslant 15 0 & \text { otherwise } \end{cases}$$
Show that \(\mathrm { E } ( X ) = 30 \ln 1.5\).
Find the median of \(X\). Find also the probability that \(X\) lies between the median and the mean.