3. An insurance company has two divisions, auto and property. Total annual claims, X, in the auto division follow a normal distribution with mean 10 and standard deviation 3. Total annual claims, Y, in the property division follow a normal distribution with mean 12 and standard deviation 4. Assuming that X and Y are independent, determine the probability that total overall claims X+Y will not exceed 29.
4. A company insures home in three cities, J, K, and L. Since sufficient distance separates the cities, it is reasonable to assume that the losses occurring in these cities are independent. The moment generating functions for the loss distributions of the cities are M2(t) = (1 - 2t)^-3, Mk(t) = (1-2t)^-2.5, Ml(t) = (1 -2t)^-4.5. Let X be the combined losses from the three cities.
(a) Find the 95th percentile of X or equivalently find c such that P(X<c) =.9
(b) Calculate E(X^2)
Please see the attached files.
From the given information, the losses in three cities are J, K and L, ...
This solution answers probability and statistics problems related to insurance.