Expectation of minimum set of i.i.d random stopping times with the same distribution

Question

What is the expectation of the minimum set of n i.i.d random stopping times? is it \frac{T}{n}

What is the distribution of the i.i.d. random stopping times? — JimmyK4542, Jun 10 '14 at 21:28
a general distribution. Does E(min(r1,r2,…rn))=E(r)/n holds for any distribution? — user156391, Jun 11 '14 at 09:03

score 0 · Answer 1 · answered Jun 10 '14 at 23:43

Not only is that answer not true in general, offhand, I can't think of any distribution of the stopping times (defined to be a distribution that is zero on $r < 0$) that would make

$E(\min(r_1, r_2, \ldots r_n)) = \frac{E(r)}{n}$

hold for all positive integer $n$.

Expectation of minimum set of i.i.d random stopping times with the same distribution

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