A sampling (coupon collector's) problem. A pack of cards consists of s identical series, each containing n
Question:
A sampling (coupon collector's) problem. A pack of cards consists of s identical series, each containing n cards numbered 1, 2,..., n. A random sample of rn cards is drawn from the pack without replacement. Calculate the probability u, that each number is represented in the sample. (Applied to a deck of bridge cards we get for s = 4, n = 13 the probability that a hand of cards contains all 13 values; and for s = 13, n = 4 we get the probability that all four suits are represented.) ==13. Continuation. Show that as so one has u, po(r, n) where the latter expression is defined in (2.3). This means that in the limit our sampling becomes random sampling with replacement from the population of the numbers 1, 2, ..., n.
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An Introduction To Probability Theory And Its Applications Volume 1
ISBN: 9780471257110
3rd Edition
Authors: William Feller