試題詳解

227. For a certain insurance company, 10% of its policies are Type A, 50% are Type B, and 40% are Type C.
The annual number of claims for an individual Type A, Type B, and Type C policy follow Poisson distributions with respective means 1, 2, and 10.

Let X represent the annual number of claims of a randomly selected policy.

Calculate the variance of X.
(A) 5.10
(B) 16.09
(C) 21.19
(D) 42.10
(E) 47.20