69. In the match problem, say that (i, j), i < j, is a pair if i

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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) Find the expected number of pairs.

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

Hint: Use the cycle concept.

(c) Use the recursion of part

(b) to find Q8.

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Introduction To Probability Models

ISBN: 9780123756862

10th Edition

Authors: Sheldon M Ross

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Question Posted: Sep 16, 2024 03:01 AM

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69. In the match problem, say that (i, j), i < j, is a pair if i

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Introduction To Probability Models

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