Coupons are collected one at a time (independently and
with replacement) from a population containing N distinct types.
This process is repeated until all N different types (coupons)
have been collected (at least once). Recently, interesting results have been
published regarding the asymptotics of the moments and the variance, of the
number TN of coupons that a collector has to buy in order to find all N
existing different coupons as N--- 00 . Moreover, the limit
distribution of the random variable TN (appropriately normalized), has
been obtained for a large class of coupon probabilities (see, , , and
). This classical problem of probability theory has found a plethora of applications
in many areas of science, and quite recently, it has been highly involved with
cryptography. In this note we take advantage of the above results and present
in detailed various examples that illustrate problems similar to those one
faces in the real life. We also conjecture on the minimum of the variance V [TN].