7. A continuous random variable \(X\) has probability density function \(f\) given by
$$f ( x ) = \left\{ \begin{array} { c }
\frac { x ^ { 2 } } { a } + b , \quad 0 \leq x \leq 4
0 \quad \text { otherwise }
\end{array} \right.$$
where \(a\) and \(b\) are positive constants. It is given that \(P ( X \geq 2 ) = 0.75\).
i. Show that \(a = 32\) and \(b = \frac { 1 } { 12 }\).
ii. Find \(E ( X )\).
iii. Find \(P ( X > E ( X ) \mid X > 2 )\)
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