Gap between two uniforms

Let X,YX,Y be independent U[0,1]U[0,1]. What is E ∣X−Y∣E\,|X-Y|? (to 3 decimals)

Show hints (2)+
  1. Integrate over the unit square.
  2. Exploit symmetry to integrate over y < x and double.

Answer

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0.3333 (± 0.005)

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