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I have some question about probabilistic combinatorial maximization as follows:

Let X = {X_1, ..., X_n} be a set of i.i.d. positive random variables,

S = {s_i} be a set of all combinations of selecting m r.v.'s from X, and

Y(s_i) = the sum of r.v.'s in the combination s_i .

I would like to evaluate the expectation of max_{s_i \in S} Y(s_i) or find out its distribution.

Since I am not sure what this type of problem is called, I have not been able to search for the solution. Any help or pointer is appreciated. Thank you so much.

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# Question about probabilistic combinatorial maximization

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