4 The random variable \(Y\) is the sum of two independent observations of the random variable \(X\). The probability generating function \(\mathrm { G } _ { Y } ( \mathrm { t } )\) of \(Y\) is given by $$G _ { Y } ( t ) = \frac { t ^ { 2 } } { ( 4 - 3 t ) ^ { 4 } }$$

1. Find \(\mathrm { E } ( \mathrm { Y } )\).
2. Write down an expression for the probability generating function of \(X\).
3. Find \(\mathrm { P } ( X = 4 )\).