Collector''s problem, Advanced Statistics

Collector's problem: A problem which derives from the schemes in which packets of a particular brand of coffe, cereal etc., are sold with coupons, cards, or other tokens. There are say n different cards that make up the complete set, every packet is sold with one card, and a priori this card is similarly to be any one of the n cards in set. Of principal interest is the distribution of N, the number of the packets which a typical customer must buy to attain a complete set. The cumulative probability distribution of N

can be shown as

1669_collectors problem.png 
1405_collectors problem1.png 


the expected value of N is given as follows
825_collectors problem2.png

 

 

Posted Date: 7/26/2012 6:47:13 AM | Location : United States







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