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