There is a given Z nonnegative numbers x1, x2, .... , xZ such that
(the Σ b=1 to Z yields xb=1.)
There is also empty set O, and for b from 1 to Z, with a probability xb, we add item b to O; the process that we add b to our set is independent from the process that we add a different item b'(b prime):
1. Come up with an expression that the probability of Z will still be null after this.
2. At the end of this procedure, what is the expected size of Z?