5. The continuous random variable \(X\) has probability density function given by $$f ( x ) = \begin{cases} \frac { 4 } { 3 x ^ { 3 } } & 1 \leq x < 2
\frac { 1 } { 12 } x & 2 \leq x \leq 4
0 & \text { otherwise } \end{cases}$$ a) Find the upper quartile of \(X\).
b) Find \(\mathrm { P } \left( \frac { 1 } { 2 } < X \leq 3 \right)\)
c) Find the value of \(a\) for which \(\mathrm { E } \left( X ^ { 2 } \right) = a \mathrm { E } ( X )\).