6 A random variable \(X\) has probability density function f . The graph of \(\mathrm { f } ( x )\) is a straight line segment parallel to the \(x\)-axis from \(x = 0\) to \(x = a\), where \(a\) is a positive constant.
- State, in terms of \(a\), the median of \(X\).
- Find \(\mathrm { P } \left( X > \frac { 3 } { 4 } a \right)\).
- Show that \(\operatorname { Var } ( X ) = \frac { 1 } { 12 } a ^ { 2 }\).
- Given that \(\mathrm { P } ( X < b ) = p\), where \(0 < b < \frac { 1 } { 2 } a\), find \(\mathrm { P } \left( \frac { 1 } { 3 } b < X < a - \frac { 1 } { 3 } b \right)\) in terms of \(p\).