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Spread of a two-card sum

EasyRandom VariablesStatistics~3m

Two identical decks each hold 55 cards labelled 0,1,2,3,40, 1, 2, 3, 4. You draw one card from each deck and add the labels. What is the standard deviation of the sum?

Show hints (2)+
  1. Variance of a discrete uniform on {0,…,4}\{0,\dots,4\} is (52−1)/12=2(5^2-1)/12 = 2.
  2. Independent draws: variances add to 44; take the square root.

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Asked at: IMC, SIG

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