Looking for a probability distribution Recently I discussed an experiment with a friend. Assume we start a random experiment. At first there is an array with size $100,000$, all set to $0$. We calculate at each round a random number modulo $2$ and select one random position in that array. If the number in the array is $1$, nothing is changed and otherwise the pre-computed value is set. The question is: how many distinct hash values would we have added in $1$%, $5$%, $50$%, $95$%, $99$% of all cases?
Example: $4$ rounds with array of size $10$:
Array                     Position   random number
[0,...,0]                    5              0
[0,...,0]                    7              1
[0,...0,1,0,0,0]             6              1
[0,..0,.1,1,0,0,0]           6              0
[0,..0,.1,1,0,0,0]           2              0

First we considered this a somehow simple problem, but after thinking for some hours, searching the web, and asking some math students, we couldn't find a solution. Do you know a probability distribution for this problem? 
Remark: Was also posted on Math Overflow and got its answer there.
 A: As answered by T. on MathOverflow.

This is equivalent to (among other
  names) the Coupon Collector problem.
  Your are asking about the distribution
  of the number of coupons collected
  after t steps, when the total number
  of possible coupons is n. 
http://en.wikipedia.org/wiki/Coupon_collector%27s_problem
ADDED: this and related distributions
  are also studied under other names
  such as Birthday Problem, random
  mappings, and random hashing.
  Kolchin-Sevastyanov-Chistyakov Random
  Allocations, Knuth The Art Of Computer
  Programming, vol. 2, and Flajolet &
  Sedgwick Analytic Combinatorics all
  discuss these problems and may contain
  the precise asymptotics of the
  distribution you are looking for.
III.10 in Flajolet and Sedgewick gives
  the Poisson answer $1−\exp(−t/n)$ when
  the ratio is held constant, but other
  asymptotic regimes are also of
  interest especially in hashing
  problems. Birthday problem is when
  $t=O(n^{1/2})$ and one gets statistics
  of the number of collisions. For t=n^k
  with 1/2

