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Math Help - Expectation -1

  1. #1
    Yan
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    Expectation -1

    Let X and Y be two independent indicator random variables, with
    P(X=1)=p and P(Y=1)=r. Find E[(X-Y)^2] in terms of p and r.
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  2. #2
    Flow Master
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    Quote Originally Posted by Yan View Post
    Let X and Y be two independent indicator random variables, with
    P(X=1)=p and P(Y=1)=r. Find E[(X-Y)^2] in terms of p and r.
    Pr(X = 1) = p and Pr(X = 0) = 1 - p.
    Pr(Y = 1) = r and Pr(Y = 0) = 1 - r.

    E[(X - Y)^2] = E[X^2 - 2XY + Y^2] = E[X^2] + E[Y^2] - 2 E[XY].

    E(X) = (1)(p) + (0)(1-p) = p.
    E(Y) = r.
    E(XY) = (1)(pr) + (0)(1 - pr) = pr.
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