(no subject)

Sam Cox ( samcox@mindspring.com )
Thu, 5 Nov 1998 15:40:39 -0400

You are refering to questions 8 and 9.
Let the classes be denoted by 1 for liability and 2 for property. Let Z be
a random risk. Z = X (C=1) with probability 0.75 and Z = Y (C=2) with
probability 0.25.

For 8 use the appendix to calculate the conditional moments:
Var(Z|C) = 20000 (C=1) or 750000 (C=2)
E[Z|C] = 100 (C=1) or 500 (C=2)
Now use the formula
E[Z] = E(V(Z|C)) + V(E(Z|C)) = 20000(0.75) + 750000(0.25) + (500 -
100)^2(0.25)(0.75) = 232,500 Answer C.

For 9 use Bayes theorem:

Pr(C=1|Z=k) = Pr(Z=k|C=1)Pr(C=1)/Pr(Z=k)