Question

The number of eggs,X, laid by the female tawny owl (Strix Aluco) has the probability distribution given in the following table

X 2 3 4
P(X=x) 0.1 0.2 0.7


For any egg, the probability that it is hatched is 0.8, independent of all other eggs . Let Y denote the number of hatched eggs in a randomly chosen nest.

(a). Obtain the probability distribution of Y
(b). Find E(Y) and Var( Y).