Expected length?

**Nappy** · May 11th 2010, 05:08 AM

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?

**Anonymous1** · May 11th 2010, 05:36 AM

[]EDIT[] $\color{red}{\text{Please delete.}}$

**Anonymous1** · May 12th 2010, 09:47 AM

I think an easier approach is:

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

Assuming......

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

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

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