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...
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?