Let X1,X2∼Exp(1)X_1, X_2 \sim \text{Exp}(1)X1,X2∼Exp(1) independently. What is the distribution of X1X1+X2\frac{X_1}{X_1 + X_2}X1+X2X1?
Beta(1,1)(1, 1)(1,1)
Uniform(0,1)(0, 1)(0,1)
Beta(1,2)(1, 2)(1,2)
Beta(2,2)(2, 2)(2,2)