Suppose that Y1 and Y2 are independent exponentially distributed random variables, both with mean B, and define U1=Y1+Y2 and U2=Y1/Y2 a, show that the joint density of (U1,U2 is FU1,U2 (U1,U2) = (1/bexp2) u1 e exp(-u1/b) 1/(1+u2)exp2, 0 smaller then u1, 0smaller then u2 o elsewhere b. are u1 and u2 independent? Solution i think there is something missing in the question. can u please coment on it whether if its true.

1. Suppose that Y1 and Y2 are independent exponentially distributed random variables, both with
mean B, and define U1=Y1+Y2 and U2=Y1/Y2 a, show that the joint density of (U1,U2 is
FU1,U2 (U1,U2) = (1/bexp2) u1 e exp(-u1/b) 1/(1+u2)exp2, 0 smaller then u1, 0smaller then
u2 o elsewhere b. are u1 and u2 independent?
Solution
i think there is something missing in the question. can u please coment on it
whether if its true