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Stats question: Item collection

  • Thread starter dreamspace
  • Start date
  • #1
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Homework Statement



Suppose that I'm collecting cards, and that in a complete collection there are m items.
When buying a new card, there's an equal probability that the card is any of those m cards.

Let X be the number of cards I need to buy in order to get a complete collection

What is the Expectation/Ex of X? What is the Standard Deviation?

Homework Equations



Let [itex]X = \sum^{m}_{i=1} X_{i} [/itex], where [itex] X_{i} [/itex] is the number of cards I need to buy in order to get a new type of card when I already have i - 1 different types of cards


The Attempt at a Solution



I figure this problem would involve probability mass function, but to be honest I'm stuck as I haven't had any probability or stats in over 10 years.

Any good pointers on how to go on with this problem?
 

Answers and Replies

  • #2
lanedance
Homework Helper
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haven't worked it, but say you have n>m cards, then what is the probability of having m different cards might be a place to start...
 
  • #3
11
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After doing some reading, this looks like something that falls under Geometric Distribution. Correct?
 
  • #4
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,705
1,722

Homework Statement



Suppose that I'm collecting cards, and that in a complete collection there are m items.
When buying a new card, there's an equal probability that the card is any of those m cards.

Let X be the number of cards I need to buy in order to get a complete collection

What is the Expectation/Ex of X? What is the Standard Deviation?

Homework Equations



Let [itex]X = \sum^{m}_{i=1} X_{i} [/itex], where [itex] X_{i} [/itex] is the number of cards I need to buy in order to get a new type of card when I already have i - 1 different types of cards


The Attempt at a Solution



I figure this problem would involve probability mass function, but to be honest I'm stuck as I haven't had any probability or stats in over 10 years.

Any good pointers on how to go on with this problem?
Google the Coupon Collector's Problem.

RGV
 

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