2 The probability generating function, \(\mathrm { G } _ { Y } ( t )\), of the random variable \(Y\) is given by $$G _ { Y } ( t ) = 0.04 + 0.2 t + 0.37 t ^ { 2 } + 0.3 t ^ { 3 } + 0.09 t ^ { 4 }$$

1. Find \(\operatorname { Var } ( Y )\).
   The random variable \(Y\) is the sum of two independent observations of the random variable \(X\).
2. Find the probability generating function of \(X\), giving your answer as a polynomial in \(t\).