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If there's n different coupons. Instead of ordering coupons one-by-one until you collect all n coupons as in the traditional 'Coupon Collector Problem', what if the coupons came in packs of m coupons. (given that the coupons are placed in the pack at random from the n coupons and are independent of each other). If random variable X is the total number of distinct coupons that one receives.

What is the expected value $E(X)$? (by using indicator random variables)

So given that one has already collected i coupons I was able to calculate the expected value of orders required to receive a new distinct coupon is $E(X_i)=\frac{n}{n-i}$ (according to the traditional 'Coupon Collector's Problem'). So now since the coupons are coming in packs of m, its pretty much the same as having m individual orders. And so I was thinking that the expected value of distinct coupons now is:

$E(X)=\frac{m}{E(X_i)}$ ?

Evelyn
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  • Sorry if I posted this twice, wondering if a fresh post would get any attention. – Evelyn Mar 29 '14 at 19:59
  • See: http://math.stackexchange.com/questions/188889/expiring-coupon-collectors-problem?rq=1 – alvonellos Mar 29 '14 at 20:06
  • You should not post the same question twice (the other is http://math.stackexchange.com/questions/730914/extension-to-the-coupon-collector-problem ) – Henry Mar 30 '14 at 00:01
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    Another related question: http://math.stackexchange.com/questions/131664/coupon-collector-problem-with-batched-selections – Henry Mar 30 '14 at 00:02

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