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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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Median of cardinality of set union

It turns out there is a (somewhat absurd) counterexample. Consider $U=\{1,2,3,4,5,6\}$, $S_1 = \{1\}, S_2 = \{2\}, S_3 = \{3,4,5,6\}$. Then $f_{\mathbf{S}}(1) = \text{median}\{1,1,4\}=1$, yet $f_{\mat …
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