Prove that if the joint cdf of X and Y satisfies Fx,y(x,y) = FX(X)FY(y), then for any
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Fx,y(x,y) = FX(X)FY(y),
then for any pair of intervals (a, b), and (c, d),
P(a < X < b, c < Y < d) = P(a < X < b)P(c < Y < d).
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