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}

Answer 1

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 $n$.