Expected length?

Jan 2010
43
0
Two points, X and Y , are chosen at random on a rod of length 1. What is the expected distance between these two points?

Can anyone help me out with this question? Not exactly sure where to start?
 
Nov 2009
517
130
Big Red, NY
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Last edited:
Nov 2009
517
130
Big Red, NY
I think an easier approach is:

\(\displaystyle E(|X-Y|) =\int \int |X-Y|f_{X,Y} dxdy\)

Assuming......

\(\displaystyle X\) ~ \(\displaystyle \text{Uniform(0,1);}\) \(\displaystyle Y\) ~ \(\displaystyle \text{Uniform(0,1) i.i.d.}\)

......makes this fairly simple, actually.