Lets assume we have a box with 45 coupons labeled 1-45. Now in this case I would like to adjust the CCP such that I can calculate the expected value (amount of draws necessary) to collect 10 specific items. For example item 1-10. How do I adjust my model such that I can calculate the amount of draws necessary to collect each item n times.

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Brennen Bishop · Accepted Answer

Let       X    n   be the number of draws it takes to draw the       n          t      h       desired item from the box after having drawn       X          n      −      1       (      X    1   is just the number of draws to draw the first item). For example       X    5   is the number of draws it takes to draw the fifth item after the fourth item.Then the number of draws,   X, necessary to draw all the desired items satisfies,  X  =      ∑          n      =      1          10        X    n    .And consequently,  E  [  X  ]  =      ∑          n      =      1          10    E  [      X    n    ]  .The probabiltiy of drawing the first desired item on each draw is       p    1    =      10    45   . So       X    1    ∼  Geometric  (      10    45    ). Can you find the form of the rest of the       X    n   to compute the above sum? If you want to collect each of the 10 desired items k times, do you see how you can extend the work provided here?

Waylon Ruiz · Accepted Answer

Yes, that helps. if I solve with recursion I get E[X] ~131,8.

Lets assume we have a box with 45 coupons labeled 1-45. Now in this case I would like to adjust the

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