# Expected length?

#### Nappy

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

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#### Anonymous1

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.