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Find a recursive equation

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Reference no: EM131680457

Question: 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.

(a) Find a recursive equation expressing pij in terms of pi-1,j and pi-1,j-1, for i2 and 1 ≤ j ≤ n.

(b) Describe how the recursion from (a) can be used to calculate pij.

Reference no: EM131680457

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