Let Y represent the variable of claim type. Suppose that there are four types of claims Y = {A, B, C} with P(A) = 0.27, P(B) = 0.41, P(C) = 0.32. Suppose that given a claim type, the number of claims, X, follows a Poisson distribution with mean . For type A claims, = 0.6. For type B claims, = 1.4. For type C claims, = 2.7. Find the expected value and variance of X.