Expected median of three dice

MediumProbability Expected Value~4m

Three fair $6$ -sided dice are rolled. What is the expected value of the median of the three?

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The map $v\mapsto 7-v$ is a symmetry that sends the median $M$ to $7-M$ .
So $\mathbb{E}[M]=\mathbb{E}[7-M]$ , forcing $\mathbb{E}[M]=3.5$ .

Answer

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3.5

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