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?
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.