5 The discrete random variable \(X\) has moment generating function \(\frac { 1 } { 4 } \mathrm { e } ^ { 2 t } + a \mathrm { e } ^ { 3 t } + b \mathrm { e } ^ { 4 t }\), where \(a\) and \(b\) are constants. It is given that \(\mathrm { E } ( X ) = 3 \frac { 3 } { 8 }\).

1. Show that \(a = \frac { 1 } { 8 }\), and find the value of \(b\).
2. Find \(\operatorname { Var } ( X )\).
3. State the possible values of \(X\).