Question: In certain situations the hypergeometric distribution can be approximated by a Poisson distribution. Suppose that w white balls and b black balls occupy a box.

In certain situations the hypergeometric distribution can be approximated by a Poisson distribution. Suppose that w white balls and b black balls occupy a box. If you extract n

α=1 Xα. Show that you can construct a coupling by performing the sampling experiment in the usual way. If white ball α

does not show up, then randomly take one of the balls extracted and exchange it for white ball α. Calculate an explicit Chen-Stein bound, and give conditions under which the Poisson approximation to S will be good.

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