00:01
So this question we have x is the total time for arrival to completion, blah, blah, blah.
00:07
F of x and y is e to minus x for y between 0 and x and x between y and infinity, and zero otherwise.
00:21
Then we're going to find that u is x minus y.
00:26
So we want to find the pdf of u.
00:28
So first of all, f of u is the probability that u is less than or equal to.
00:36
Sum value u.
00:40
So this is going to be basically the probability that x minus y, x minus y is less than or equal to u, which is the probability that x is less than or equal to u plus y.
00:57
So what we're going to do is we're going to integrate.
01:00
So we integrate from y is equal to 0 up to infinity and we integrate from x is equal to y up to y plus u.
01:14
Dx and then the joint pdf there.
01:21
So let's integrate it.
01:22
So integrate from 0 to infinity, dy.
01:25
Integrate this with respect to x.
01:27
We're just going to get e to the minus y minus e to the minus y plus u, which we then integrate dy...