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What is the probability mass function of the sum of $n$ i.i.d categorical variables, $X_i$, each taking values $0,1,2$ with probability $(1-p)^2, 2p(1-p), p^2$, respectively?

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    Like @Dilip said, or, for a zero-cleverness solution, use [probability generating functions](http://en.wikipedia.org/wiki/Probability-generating_function).2012-02-09

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