(Answered) Question there are n types of toys which you are collecting

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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 i^th toy, you have exactly j toy types in your collection, for i ≥ 1 and 0 ≤ j ≤ n.

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

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

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