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Distributionshard
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Let X1,X2X_1, X_2X1​,X2​ be two independent random variables where X1∼Gamma(2,1)X_1 \sim \text{Gamma}(2, 1)X1​∼Gamma(2,1) and X2∼Gamma(3,1)X_2 \sim \text{Gamma}(3, 1)X2​∼Gamma(3,1). What is the distribution of the ratio Y=X1X1+X2Y = \frac{X_1}{X_1 + X_2}Y=X1​+X2​X1​​?