At a wedding reception on an evening the representative of the host is taking it as an occasion to exercise and explain a classical analytic problem. specifically, he insists that he would start serving the food only when the first table, which is arranged for 12 guests to dine together, has guests born in every twelve months of the year. assume that any given guest is equally likely to be born in any of the twelve months of the year, and that new guests were arriving at every two minutes then. what is the expected waiting time of the first arriving guest before the food gets served eventually?

Since this looked like a Coupon Collector's problem variation, my initial approach was to determine the sum of the expected value of each guests of unique birth months.

X ~ FS(p) [First Success Distribution]

X = time needed until food gets served

$$ E[X] = E[X1] + E[X2] + ... + E[X12] $$

$$ => E[X] = 12/12 + 12/11 + ... + 12/1 $$

However, this is where i ran into problem, since I don't know how to handle the arrival at every two minutes in my equation. Should I just multiply by 2? Or am i missing something very obvious or basic trivia? Help will be appreciated.



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