# Stats question: Item collection

1. Sep 24, 2012

### dreamspace

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

Let $X = \sum^{m}_{i=1} X_{i}$, where $X_{i}$ 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

3. 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?

2. Sep 24, 2012

### lanedance

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. Sep 24, 2012

### dreamspace

After doing some reading, this looks like something that falls under Geometric Distribution. Correct?

4. Sep 24, 2012