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Math Help - expected number of coupons

  1. #1
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    Exclamation expected number of coupons

    suppose there are N different types of coupons and each time one obtains a coupon, it is equally likely to be any one of the N types. Find the expected number of coupons one needs to collect before obtaining a complete set of atleast one of each type
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    what have you done so far?
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  3. #3
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    i let X= the # of different types of coupons in a set of n coupons and X(i)= type of coupon but i honestly have no clue how to set this problem up or execute it.
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    MHF Contributor harish21's Avatar
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    Let X denote the number of coupons collected before a complete set is attained.

    Let X_i \;\;i=0,\cdots,N-1 be the number of additional coupons that need to be obtained after i distinct types have been collected in order to obtain another distinct type.

    So, X=X_0+X_1+\cdots+X_{N-1}

    when you have collected i distinct coupons, you will obtain a new coupon with a probability of \dfrac{N-i}{N}

      P(X_i = k)= \bigg(\dfrac{N-i}{N}\bigg)\;\bigg(1-\dfrac{N-i}{N}\bigg)^{k-1}\;\;\; k\geq 1,

    figure out what distribution this is and find its expected value.
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  5. #5
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    Quote Originally Posted by nikie1o2 View Post
    suppose there are N different types of coupons and each time one obtains a coupon, it is equally likely to be any one of the N types. Find the expected number of coupons one needs to collect before obtaining a complete set of atleast one of each type
    Coupon collector's problem - Wikipedia, the free encyclopedia
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