Question: Let X1 GAM(1,), X2 GAM(2,), X3 GAM(3,) be independent random variables. Find constant a such that variable Y = aX1/(X2 + X3)

Let X1 ∼ GAM(1,λ), X2 ∼ GAM(2,λ), X3 ∼ GAM(3,λ) be independent random variables. Find constant a such that variable Y = aX1/(X2 + X3) has an F distribution.

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