\(6 Y\) is a discrete random variable which takes the values \(0,2,4, \ldots\) The probability generating function of \(Y\) is given by
\(\mathrm{G}_{Y}(t)=\frac{k}{1-a t^{2}}\)
(a) Find \(k\) in terms of \(a\).

(b) Show that \(\mathrm{P}(Y\gt 2)=a^{2}\).

It is now given that \(a=0.2\).
(c) Find the value of \(\mathrm{E}(Y)\).