Transformations & Jacobians · Statistics Graduate Level

Statistics Graduate Level Quiz

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Let

X\sim\operatorname{Gamma}(a,\lambda)

and

Y\sim\operatorname{Gamma}(b,\mu)

be independent, where the second argument is a rate. Define

U=X+Y

and

V=X/(X+Y)

. Under which condition are

U

and

V

independent?

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