This week the number X of claims coming into an insurance office is Poisson with mean 100. The probability that any particular claim relataes to automobile insurance is .6, independent of any other claim. If Y is the number of automobile claims, then Y is binomial with X trials, each with “success” probability .6.

a. Determine E(Y|X = x) and V(Y|X = x).
b. Use part (a) to find E(Y).
c. Use part (a) to find V(Y).