Let r.v.s X and Y be independent, Z 1 = X +Y, Z 2 = X Y.

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Let r.v.’s X and Y be independent, Z1 = X +Y, Z2 = X −Y. When are the r.v.’s Zand Z2 uncorrelated? Would it mean that they are independent? Let, say, (X,Y) be uniformly distributed on the square {(x,y) : |x| ≤ 1, |y| ≤ 1}. If we know X +Y, does it give an additional information about X −Y?)

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