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In class I went over the proof that the expected value of
the negative binomial NB(r,p) is
by writing it as the sum of r geometric (p) random variables.
I showed how one would compute the
expected number of cereal boxes to buy
if there were N objects to be collected:
And the number of matches in the matching problem
can be put as the sum of the indicator variables Xi where Xi=1
if the ith person gets his/her hat.
this link for the matching problem applet