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Expected median of three dice

MediumProbabilityExpected Value~4m

Three fair 66-sided dice are rolled. What is the expected value of the median of the three?

Show hints (2)+
  1. The map v↦7−vv\mapsto 7-v is a symmetry that sends the median MM to 7−M7-M.
  2. So E[M]=E[7−M]\mathbb{E}[M]=\mathbb{E}[7-M], forcing E[M]=3.5\mathbb{E}[M]=3.5.

Answer

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3.5

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Asked at: Optiver, Akuna Capital

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