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This question already has an answer here:

I am trying to find the distribution of the maximum of a set of four continuous independent random variables that have a general distribution.

I have found resources that discuss how to find such a distribution when the probability density function is known, but I am curious to know the generalized solution.

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marked as duplicate by kjetil b halvorsen, Michael Chernick, Peter Flom Jun 13 '18 at 20:59

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  • $\begingroup$ There is the 3 types theorem of Gnedenko for iid random variables. Extensions to dependence cases are given in Leadbetter;s book to name one. $\endgroup$ – Michael Chernick Jun 12 '18 at 15:25
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The general solution is exactly the same as a particular solution. $$P(\max_i X_i \leq t) = \prod_i P(X_i \leq t) = \prod_i F_{X_i}(t).$$

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