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Competitive Stats
Q107Section C (Part C)107 of 120

Extreme values — the Gumbel limit for exponential maxima

Let {Xn:n≥1}\{X_n:n\ge1\} be a sequence of independent and identically distributed random variables, where X1X_1 has an Exponential distribution with mean 1. Define Tn=max⁡{X1,X2,…,Xn}−ln⁡nT_n=\max\{X_1,X_2,…,X_n\}-\ln n, n≥1n\ge1. Suppose Tn→dYT_n\stackrel{d}{\to}Y as n→∞n\to\infty. Then which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Options

Select every correct option, then submit.