- A random variable \(X\) has probability density function
$$f ( x ) = \begin{cases} \frac { 2 x } { 15 } & 0 \leqslant x \leqslant k
\frac { 1 } { 5 } ( 5 - x ) & k < x \leqslant 5
0 & \text { otherwise } \end{cases}$$
- Showing your working clearly, find the value of \(k\).
- Write down the mode of \(X\).
- Find \(\mathrm { P } \left( \left. X \leqslant \frac { k } { 2 } \right\rvert \, X \leqslant k \right)\)
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