Consider a collection of n individuals. Assume that each person’s birthday is equally likely to be any of the 365 days of the year and also that the birthdays are independent. Let Ai,j, i ≠ j, denote the event that persons i and j have the same birthday. Show that these events are pairwise independent, but not independent. That is, show that Ai,j and Ar,s are independent, but the
events Ai,j, i ≠ j are not independent.
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