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Consider the standard balls and bins process. A collection of m identical balls are thrown into n bins: each ball is thrown independently into a bin chosen uniformly at random.
(a) What is the (precise) probability that a particular bin i contains exactly k balls at the end of the experiment?
(b) Suppose m = n. Let Y be the number of bins that are empty. What is the expectation of Y?
(c) What is the variance of Y?
Explain your calculations when you derive the bounds.
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