8 The continuous random variable \(X\) has cumulative distribution function \(\mathrm { F } ( x )\) where
$$\mathrm { F } ( x ) = \begin{cases} 0 & x = 0
\mathrm { e } ^ { k x } - 1 & 0 \leq x \leq 5
1 & x > 5 \end{cases}$$
8
- Show that \(k = \frac { 1 } { 5 } \ln 2\)
[0pt]
[2 marks]
8 - Show that the median of \(X\) is \(a \frac { \ln b } { \ln 2 } - c\), where \(a , b\) and \(c\) are integers to be found.
| 8 | Show that the mean of \(X\) is \(p - \frac { q } { \ln 2 }\), where \(p\) and \(q\) are integers to be found. |