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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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Distinguishing between urn probability models
Not perfectly, but yes.
If you remove all the balls from the urn and examine each, then mark and replace it, you will eventually examine all the balls. There will either be exactly a 70/30 split, or …