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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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What is the probability that you roll a dice with s sides for n times and t sides appeared o...
You roll a dice with $s$ sides for $n$ times. What is the probability that $t$ sides appeared once?
Example with $s=2$, $n=3$: you roll a dice with 2 sides for 3 times.
possible outcomes: '1' and '2' …