Distributionshard
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Let X1,X2X_1, X_2 be two independent random variables where X1Gamma(2,1)X_1 \sim \text{Gamma}(2, 1) and X2Gamma(3,1)X_2 \sim \text{Gamma}(3, 1). What is the distribution of the ratio Y=X1X1+X2Y = \frac{X_1}{X_1 + X_2}?