LetXandYbe independent random variables and both exponentially distributed with mean 1/. Prove that the distribution of a new random variable...
View the step-by-step solution to:

Question

# Let X and Y be

independent random variables and both exponentially distributed with mean 1/μ. Prove that the distribution of a new random variable Z= X/(X+Y)  is uniform over(0,1), i.e., prove P{Z ≤ z} = z for 0 < z ≤ 1.

Note: There are at least two ways to show this. One is to directly integrate over some domain based on the joint pdf of X, Y , and the other is to utilize the conditional expectation theorem, i.e., first to make one of X, Y constant and deal with it, and

we will use the second suggested... View the full answer

### Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

• ### -

Study Documents

Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

Browse Documents