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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Originally Posted by Yan 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. $\displaystyle E[(X - Y)^2] = E[X^2 - 2XY + Y^2] = E[X^2] + E[Y^2] - 2 E[XY]$. E(X) = (1)(p) + (0)(1-p) = p. E(Y) = r. E(XY) = (1)(pr) + (0)(1 - pr) = pr.
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