Spread of a two-card sum

EasyRandom Variables Statistics~3m

Two identical decks each hold $5$ cards labelled $0, 1, 2, 3, 4$ . You draw one card from each deck and add the labels. What is the standard deviation of the sum?

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

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Spread of a two-card sum

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