8 The continuous random variable \(X\) has probability density function
$$f ( x ) = \begin{cases} k \sin 2 x & 0 \leq x \leq \frac { \pi } { 6 }
0 & \text { otherwise } \end{cases}$$
where \(k\) is a constant.
8
- Show that \(k = 4\)
8 - Find the cumulative distribution function \(\mathrm { F } ( x )\)
8 - Find the median of \(X\), giving your answer to three significant figures.
8
- Find the mean of \(X\) giving your answer in the form \(\frac { 1 } { a } ( b \sqrt { 3 } - \pi )\) where \(a\) and \(b\) are integers.
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