The length of time that a machine operates without failure is denoted by X and the length of time to repair a failure is denoted by Y.
X and Y are independent each with exponential ditribution, mean 1.
Find the pdf of U = X/[X + Y], the proportion of time that the machine is in operation during any one operation-repair cycle.
Use the pdf of U to find the probability that U is greater than 0.75.