toss balls one at a time into n bins, each ball will always land in one of the n bins.
stop tossing once some bin end up with 2 balls. and the tosses are independent of each other
X be the number of tosses needed.
(so X is between 2 and n+1)
find E(X)
i find linearity hard to apply here.
and the naive definition resulted in a messy sum, that i cannot reduce to simple form.
is this a well know distribution somewhere?
thanks for any insights
I calculated a couple of values with Wolfram|Alpha:
Then I made a log-log-plot in excel which showed a straight line.Code:n EX 1 2 10 4.6 100 13.2 1000 40.3 10000 125.66
I used excel's solver to find the coefficients.
The resulting approximation is:
Code:n EX Approx 1 2 2 10 4.6 4.702847075 100 13.2 13.25 1000 40.3 40.27847075 10000 125.66 125.75