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Unformatted text preview: k ( y 1 ,...,y k ) = = f X 1 ,...,X k T1 ( y 1 ,...,y k ) J T1 ( y 1 ,...,y k ) . Example : Let X 1 and X 2 be independent standard exponential random variables, and let Y 1 = X 1 + X 2 , Y 2 = X 1 /X 2 . Find the joint pdf of Y 1 and Y 2 . The range of Y 1 ,Y 2 might be the issue. Example Let ( X 1 ,X 2 ) be continuous with a joint pdf f X 1 ,X 2 ( x 1 ,x 2 ) = ( 1 if 0 < x 1 ,x 2 < 1 0 otherwise. Let Y 1 = X 1 + X 2 , Y 2 = X 1X 2 . Find the joint pdf of ( Y 1 ,Y 2 )....
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 Fall '10
 SAMORODNITSKY

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