Help with this question from casella and berger?

10.18 For the situation of Exercise 10.2.1, that is, if X1, X2, ..., Xn are iid, where Xi ~ n(u, 2) with probability 1 -8 and X, ~ f(r) with probability 8, where f(I) is any density with mean 0 and variance 7, show that Var(X) = (1 - 8)- 02 + 8(1 - 8) (0 - #)2 n n n Also deduce that contamination with a Cauchy pdf will always result in an infinite variance. (Hint: Write this mixture model as a hierarchical model. Let Y = 0 with probability 1 - 8 and Y = 1 with probability 6. Then Var(X,) = E[Var(X,) |Y] + Var (EX. JY]).)