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IzaksonasSmith, Evan
Problem 3.4
Coupon Collectors
Problem
The famous
coupon collector problem
works as follows: every week, SuperDuperMegaMart chooses,
uniformly at random, a coupon from the set
{
C
1
,C
2
,...,C
n
}
, and sends this coupon to all of its loyal
customers. Alice desperately would like to have a complete collection of SDMM coupons, so she signs
up to join the mailing list. What is the expected number of weeks until Alice has seen all
n
coupons?
Analysis
Let us consider that each coupon must come in one at a time, and more over that we must receive the
ﬁrst coupon ﬁrst the second second and so on and so forth.
Further let us consider that since the order that the individual coupons come in matters not at all and
so out of
n
coupons there are
n
that before the ﬁrst coupon we have not seen. And with each new,
never before seen coupon, this diminishes by one.
From these two truths we can begin to unravel the problem, for if we know that we do not wait for the
k
th
coupon until the (
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This note was uploaded on 10/21/2011 for the course CSCI 5403 taught by Professor Sturtivant,c during the Spring '08 term at Minnesota.
 Spring '08
 Sturtivant,C

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