Graduate level probability homew

Here's a sample problem, there are 7 more very difficult ones like this. Does this look like something you can do? 1. A group of n people are comparing their birthdays (make the same assumptions as in the birthday problem from class, e.g., that there aren't twins and that there are 365 days in a year, all equally likely). (a) On average, how many birthdays are represented in the group, i.e., how many days are there such that someone (or more than one person) has that birthday? (b) On average, how many matches are there in the group? (Two people match if they share the same birthday. If three people have the same birthday, that counts as three matches since each pair has a match.) (c) Let n = 23. Explain intuitively why the number of matches is approximately Poisson, and state what the mean of this Poisson is. Use this Poisson approximation to show that there is about a 50% chance that there is at least one match.
User_1029 | Jul 14, 2011, 18:14 PM

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