Statistics Graduate Level Quiz
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Suppose X∼Gamma(2,θ)X\sim\mathrm{Gamma}(2,\theta) and Y∼Gamma(3,θ)Y\sim\mathrm{Gamma}(3,\theta) are independent, where both distributions use the same scale parameter. Define S=X+YS=X+Y and R=X/SR=X/S.
Which statement about the transformed variables and the conditional mean is correct?
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