Let A and B be independent events, with indicator random variables IA and IB.
a) Describe the distribution of (IA+IB)^2 in terms of P(A) and P(B).
b) What is E(IA+IB)^2?
Pr(IA = 1) = Pr(A), Pr(IA = 0) = Pr(A') = 1 - Pr(A).
Pr(IB = 1) = Pr(B), Pr(IB = 0) = Pr(B') = 1 - Pr(B).
(a) Let X = (IA + IB)^2. Then the possible values of X are X = 0, 1, 4.
What combination of IA and IB gives X = 0? Therefore Pr(X = 0) = .....
What combinations of IA and IB give X = 1? Therefore Pr(X = 1) = .....
What combination of IA and IB gives X = 4? Therefore Pr(X = 4) = .....
(b) E(X) = 0 Pr(X = 0) + 1 Pr(X = 1) + 4 Pr(X = 4) = ....