In the previous exercise, show that the distribution of Y is Poisson with mean 60. [You will need to recognize the Maclaurin series expansion for the exponential function.] Use the knowledge that Y is Poisson with mean 60 to find E(Y) and V(Y).

Data from exercise 85:

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.