N people arrive separately to a professional dinner Upon arrival
N people arrive separately to a professional dinner. Upon arrival, each person looks to see if he or she has any friends among those present. That person then sits either at the table of a friend or at an unoccupied table if none of those present is a friend. Assuming that each of the
pairs of people is, independently, a pair of friends with probability p, find the expected number of occupied tables.
Let Xi equal 1 or 0, depending on whether the ith arrival sits at a previously unoccupied table.
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