Let Y1 and Y2 have joint density function f (y1, y2) and marginal densities f1(y1) and
Chapter 5, Problem 5.43(choose chapter or problem)
Let Y1 and Y2 have joint density function f (y1, y2) and marginal densities f1(y1) and f2(y2), respectively. Show that Y1 and Y2 are independent if and only if f (y1|y2) = f1(y1) for all values of y1 and for all y2 such that f2(y2) > 0. A completely analogous argument establishes that Y1 and Y2 are independent if and only if f (y2|y1) = f2(y2) for all values of y2 and for all y1 such that f1(y1) > 0
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