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Math Help - expected value/ convergence

  1. #1
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    expected value/ convergence

    A die is rolled once. If X is the number of ones and Y is the number of sixes obtained(note that each can have only two values, 0 or 1), find:
    a. the expected value and variance of X and Y,
    b. Cov(X, Y ).

    answers (what ive done, can i get confirmation or suggestions?)


    Since only one dice is rolled, expected value for E(X) and E(Y) would both be 1/6.
    Since they are independent, E(XY) = 0

    Var(x) = (1^2)/6 - (1/6)^2 = 5/36
    Var(y) = 5/36

    Cov(XY) = E(XY) - (μx)(μy) = 0 - (1/6)(1/6) = -1/36

    is this right?
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  2. #2
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    Looks fine to me.
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