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PostPosted: Thu, 24 Nov 2016 02:58:00 UTC 
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Say you have a fair die with m sides. Show that the probability that the sum of n rolls is less than or equal to j is just

${1\over m^n}\sum_{k=0}^\infty (-1)^k{n\choose k}{j-mk\choose n}

Hint:

Spoiler:
Consider the generating function for the distribution

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