Introdution to probability models chapter 3 69 In the match

Introdution to probability models chapter 3, #69.

In the match problem, say that (i,j), i<j, is a pair if i chooses j\'s hat and j chooses i\'s hat.

(a) Let Qn denote the probability that there are no pairsand derive a recursive formula for Qn in terms of of Qj, j<n.

(b) Use the recursion of part (a) to find Q8.

Solution

Answer

Let I(i,j) equal 1 if i and j are a pair and 0 otherwise. Then,

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