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Variance of the larger of two dice

MediumRandom VariablesStatistics~5m

Two fair dice are rolled and you keep only the larger of the two faces, M=max⁡M=\max (a roll of 3 and 5 gives M=5M=5). What is the variance of MM? Give a decimal to four places.

Show hints (2)+
  1. The max is not uniform - get its pmf from P(M≤k)=(k/6)2P(M\le k)=(k/6)^2, so P(M=k)=(2k−1)/36P(M=k)=(2k-1)/36.
  2. Then Var⁡(M)=E[M2]−(E[M])2\operatorname{Var}(M)=E[M^2]-(E[M])^2.

Answer

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1.9715 (± 0.001)

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Asked at: Multi-Strategy Quant, Data-Driven Research

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