Lets say I have a geometric distribution (of the number X of Bernoulli trials needed to get a success) with parameter `p`

(success probability of a trial).

Assume I randomly sample `n`

elements from this distribution.

My problem is: what is the expected *maximum* element of such a sample (it should depend on `n`

I guess)? Hopefully it makes sense...

For `n=1`

, e.g. if I only pick a single element from the distribution, the answer would be the mean `1 / p`

of the distribution. For samples of larger cardinalities?