# Stats question: Item collection

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

## 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?

lanedance
Homework Helper
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...

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

Ray Vickson
Homework Helper
Dearly Missed

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

## 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?