There are n types of toys, which you are collecting one by one. Each time you buy a toy
Chapter 2, Problem 62(choose chapter or problem)
There are n types of toys, which you are collecting one by one. Each time you buy a toy, it is randomly determined which type it has, with equal probabilities. Let pij be the probability that just after you have bought your ith toy, you have exactly j toy types in your collection, for i 1 and 0 j n. (This problem is in the setting of the coupon collector problem, a famous problem which we study in Example 4.3.11.) (a) Find a recursive equation expressing pij in terms of pi1,j and pi1,j1, for i 2 and 1 j n. (b) Describe how the recursion from (a) can be used to calculate pij.
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