Math question

1. Let X and Y be continuous, with a joint pdf

fxy(x,y) = 15xy^2 if 0<x<1, 0<y<1, 0<y<x 0 otherwise

Let T = X-Y , U= X/Y. Find the joint density of T and U.

2. 
The length of time that a certain machine operates without failure is denoted by X1 and the length of the repair time by X2. After repair the machine is assumed to operate like new. Assume that X1 and X2 are independent standard exponential random variables. 

Find the pdf of Y= X1/(X1 + X2), 
the proportion of time that the machine is in operation during any one operation-repair cycle, by choosing another function, say, Z, of X1 and X2, computing the joint density of Y and Z, and then deriving from it the (marginal) density of Y .