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Let X and Y be discrete random variables. Show tha

Let X and Y be discrete random variables. Show that X and Y are independent if and only if fX,Y (x, y) = fX(x)fY (y) for all x and y. 6. Let X have distribution F and density function f and let A be a subset of the real line. Let IA(x) be the indicator function for A: IA(x) = 1 x ? A 0 x /? A. Let Y = IA(X). Find an expression for the cumulative distribution of Y . (Hint: first find the probability mass function for Y .)

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