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Consider the ratios U=X/Z,V=Y/Z where X,Y,Z are random variables. We first propose examples where X,Y are independent and (X,Y),Z are dependent, but U,V are independent. This is followed by an example where X,Y are dependent and (X,Y),Z are dependent, but U,V are independent. These examples broaden the scope of Mukhopadhyay and Son (2013).
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