- The continuous random variable \(X\) has cumulative distribution function
$$\mathrm { F } ( x ) = \left\{ \begin{array} { l r }
0 & x < 3
c - 4.5 x ^ { n } & 3 \leqslant x \leqslant 9
1 & x > 9
\end{array} \right.$$
where \(c\) is a positive constant and \(n\) is an integer.
- Showing all stages of your working, find the value of \(c\) and the value of \(n\)
- Find the lower quartile of \(X\)