Results 1 to 5 of 5

Math Help - Another kind of coupon collector's problem

  1. #1
    Member
    Joined
    Sep 2011
    From
    india
    Posts
    106
    Thanks
    2

    Post 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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Another kind of coupon collector's problem

    Quote Originally Posted by Vinod View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2011
    From
    india
    Posts
    106
    Thanks
    2

    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.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2014
    From
    los angles, usa
    Posts
    6

    Re: Another kind of coupon collector's problem

    Thank you all for your valuable information.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2011
    From
    india
    Posts
    106
    Thanks
    2

    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.
    Last edited by Vinod; July 11th 2014 at 07:18 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: October 23rd 2012, 10:59 PM
  2. Replies: 3
    Last Post: September 26th 2012, 12:23 PM
  3. Coupon Rate
    Posted in the Business Math Forum
    Replies: 2
    Last Post: March 25th 2010, 10:54 AM
  4. Replies: 3
    Last Post: October 15th 2009, 12:43 AM
  5. collector's choice
    Posted in the Math Challenge Problems Forum
    Replies: 3
    Last Post: January 19th 2007, 05:14 AM

Search Tags


/mathhelpforum @mathhelpforum