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 U1, . . . ,Un 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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