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February 23rd, 2012, 11:19 AM   #1
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Randomly selecting N from N

Dear all,

I am a newcomer here, but am looking for some advice. I believe this problem must be well known, but I am not sure where to look. This is a simpler version of the real problem, but I am hoping that if I can get a look at how this was solved it will help me with my real problem.

Imagine I have N equally likely choices (boxes) (I initially thought about 100, but liked the idea of generalising it), and make N independent choices, what is the most likely number of independent boxes I will fill? Once a box has been chosen it can clearly be chosen again, or else it becomes rather a boring problem. Is there anything which I can do to think about the distribution of independent boxes filled around this most likely number?

So, does anyone have any idea where I should be looking for an approach to this?

Many thanks for any help you can offer.

Mike
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February 23rd, 2012, 05:30 PM   #2
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Re: Randomly selecting N from N

A well known version of this question concerns the probability of two students, in a class of a given size, having the same birthday.
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