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Average distance on an interval

EasyRandom Variables~3m

X1X_1 and X2X_2 are two independent draws from a continuous Uniform distribution on [2,8][2, 8]. What is the expected gap between them, E∣X1−X2∣E|X_1 - X_2|? Give a decimal to two places.

Show hints (2)+
  1. The signed difference averages 00 - you need the absolute gap.
  2. For two i.i.d. Uniform[a,b][a,b] draws, E∣X1−X2∣=(b−a)/3E|X_1-X_2| = (b-a)/3.

Answer

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2 (± 0.01)

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