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Math Help - Expectation -2

  1. #1
    Yan
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    Expectation -2

    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?
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  2. #2
    Flow Master
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    Quote Originally Posted by Yan View Post
    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) = ....
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