# What is the distribution of the maximum of a set of random variables? [duplicate]

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.

• 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. – Michael R. Chernick Jun 12 '18 at 15:25

The general solution is exactly the same as a particular solution. $$P(\max_i X_i \leq t) = \prod_i P(X_i \leq t) = \prod_i F_{X_i}(t).$$