1 The independent random variables \(X\) and \(Y\) have Poisson distributions with parameters 16 and 2 respectively, and \(Z = \frac { 1 } { 2 } X - Y\).
Find \(\mathrm { E } ( Z )\) and \(\operatorname { Var } ( Z )\).
State whether \(Z\) has a Poisson distribution, giving a reason for your answer.