In addition to limit theorems that deal with sums, there
Chapter , Problem 29(choose chapter or problem)
In addition to limit theorems that deal with sums, there are limit theorems that deal with extreme values such as maxima or minima. Here is an example. Let \(U_{1}, \ldots, U_{n}\) be independent uniform random variables on [0, 1], and let \(U_{(n)}\) be the maximum. Find the cdf of \(U_{(n)}\) and a standardized \(U_{(n)}\), and show that the cdf of the standardized variable tends to a limiting value.
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