4. A continuous random variable \(X\) has probability density function $$\mathrm { f } ( x ) = \left\{ \begin{array} { c c } k ( a - x ) ^ { 2 } & 0 \leqslant x \leqslant a
0 & \text { otherwise } \end{array} \right.$$ where \(k\) and \(a\) are constants.

1. Show that \(k a ^ { 3 } = 3\) Given that \(\mathrm { E } ( X ) = 1.5\)
2. use algebraic integration to show that \(a = 6\)
3. Verify that the median of \(X\) is 1.2 to one decimal place.
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