Brad. C. Johnson

(Statistics, University of Manitoba)

On the Number of i.i.d. Samples Required to Observe All of the Balls in an Urn

Date Tuesday, November 18, 2008

Suppose an urn contains m distinct white balls, numbered 1, . . . , m, and let K1 , K2 , K3 , . . . be an independent and identically distributed (i.i.d.) sequence of positive integer valued random variables. Suppose further that, at each time i, we take a without replacement random sample of size Ki , paint any white balls in the sample red, and return them to the urn. Of interest is the number, say tau, of samples required to paint all of the balls in the urn red. When P{Ki = 1} = 1 for all i, we have the classic coupon collector's problem. In this talk I will present a brief history of this problem and focus on some approximation methods for E(tau), V(tau) and P{tau > r} when the Ki are i.i.d. and bounded.