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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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Probability that a sum is less that a given value [closed]

I don't have many skills in probability theory, so I need a little help. My problem is the following: Let $n_1,n_2,...,n_k\in[0,1,...,n]$ such as $n_1+n_2+...+n_k=n$. Which is the probability that $$ …