I have a problem that asks me to find the expected value of the maximum of 4 random variables uniformly distributed on (0,5) . If they were Uniform on (0,1), I could quickly use the expected value for the beta distribution , and get (4/5). So I just guessed to multiply this by the length of the interval and the answer is correct and takes a lot less time than finding the density and integrating. I don't know if it really makes sense, or it's just coincidence.
I don't know. I've been waiting for someone to answer this. 4 seems like it would be an intuitively correct answer. I'm guessing its not a coincidence, and the uniform distribution lets you do that. Good old uniform, lets you get away with stuff noone else will. Like the ideal stripper.
It makes sense, and it's not coincidence. You could do this with any distribution actually; its not peculiar to uniform. All you need to do is rescale the variable. If U1, U2, U3, U4 are the original variables uniform on (0,5), define Vi = Ui/5. Then the order statistics for the Vi's are beta, giving 0.8. scale back to (0,5) and you get 4.
Units are always arbitrary. There may be conventional defaults but you can always change them if it's more convenient. Just cahnge back to the units you need at the end.