Let be the order statistics of a random sample of size from a uniform distribution on the interval (0,2).
If are the uniform RVs from the sample then
However, I am not sure how to use these probabilites to find the interval I'm interested in
(The end points are not real numbers, but RVs. I tried subtraction, but I don't think thats right. Is there a different way to think of this interval?)
Thank you for your assistance.