# Thread: Another kind of coupon collector's problem

1. ## Another kind of coupon collector's problem

Hi,
Suppose there are m different types of coupons, and that each time one obtains a coupon it is equally likely to be any of these types. If X denotes the number of distinct types in a collection of n coupons, find the expected value and variance of the number of distinct types in a collection of n coupons.

2. ## Re: Another kind of coupon collector's problem

Originally Posted by Vinod
Hi,
Suppose there are m different types of coupons, and that each time one obtains a coupon it is equally likely to be any of these types. If X denotes the number of distinct types in a collection of n coupons, find the expected value and variance of the number of distinct types in a collection of n coupons.
Look at this.

3. ## Re: Another kind of coupon collector's problem

Hi Plato,
Suppose there are 20 different types of coupons. I am having a collection of 10 coupons with 5 distinct types. Now what would be expected value and variance of the number of distinct types of coupons?
I have calculated expected value =8.0253 and tried to compute variance also, but some concepts are still unclear to me.

4. ## Re: Another kind of coupon collector's problem

Thank you all for your valuable information.

5. ## Re: Another kind of coupon collector's problem

Hi members,
As $X_i$ is bernoulli random variable, we have
E[$X_i$]=1-$\left(\frac{m-1}{m}\right)**n$
What is meaning of this ?
** is a superscript symbol.