Question: Problem Let X1, X2, . . . , Xn be i.i.d. exponential(1) random variables. (a) For any real constant c, let Yn be the number

Problem Let X1, X2, . . . , Xn be i.i.d. exponential(1) random variables.

(a) For any real constant c, let Yn be the number of Xi's that are ? logn+c. Find

the limiting probability

(b) Let Vn = min(X1,...,Xn). Given any 0

Date: May 21st, 2021.

lim P (Yn ? 1) . n??

lim P(nVn >a)=p.

Problem Let X1, X2, ..., Xn be i.i.d. exponential(1) random variables. (a) For any real constant c, let Yn be the number of Xi's that are > log n + c. Find the limiting probability lim P (Yn a) = p

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