1) for continuous distributions, Var(B) = length of interval squared/12
2) when claim amounts are chosen from a list (ex: 1,2,3,2,1), Var(B) = 0
(why, since claims amounts vary from 1 to 3?)
3) Var(B) = E[B^2] - (E[B])^2
4) Var(B) = u^2
How do you decide between 1), 3), and 4)? Here is an example that does not
seem to fit any of the above:
Policyholders come in two classes. Memebers of class A have a 20% of
having a claim and when they do, the pdf of the amound is f(x) = 1/1000, 0
< x < 1000. Members of class B have a 25% chance of having a claim and
when they do, the pdf of the amount is f(x) = x/500,000, 0 < x < 1000.
Suppose 100 policies are sold to class A individuals and 50 to class B
individuals. Determine the mean and variance of total claims.
ANSWER:
For one member of class A, u = 500 and sigma^2 = 83,333.
For one member of class B, u = 666 and sigma^2 = 55,555.
They go on to solve the problem, which I can do given the above, but I
cannot calculate sigma^2 for either class A or class B.
For those of you wanting the final answers: E(S)=18,333 Var(S)=10,527,777