The Gumbel distribution is the distribution of log X with X Expo(1). (a) Find the CDF of
Chapter 5, Problem 51(choose chapter or problem)
The Gumbel distribution is the distribution of log X with X Expo(1). (a) Find the CDF of the Gumbel distribution. (b) Let X1, X2,... be i.i.d. Expo(1) and let Mn = max(X1,...,Xn). Show that Mn log n converges in distribution to the Gumbel distribution, i.e., as n ! 1 the CDF of Mn log n converges to the Gumbel CDF.
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