Scaling an exponential maximum

Topic: A first look at extremes · more questions on this topic
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For independent \mathrm{Exp}(2) variables, give a_n and b_n that produce the Gumbel limit.

Worked answer (click to show)

For an exponential rate \lambda the centring (\log n)/\lambda and the scale 1/\lambda produce the Gumbel limit. Here \lambda=2, so b_n=(\log n)/2 and a_n=1/2.