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It is required to place in order n books B₁, B2, ..., Bn on a library shelf in such a way that readers searching from left to right waste as little time as possible on average. Assuming that each reader requires book B, with probability pi, find the ordering of the books which minimizes P(Tk) for all k, where T is the (random) number of titles examined by a reader before discovery of the required book.

It is required to place in order n books B₁, B2, ..., Bn on a library shelf in such a way that readers searching from left to right waste as little time as possible on average. Assuming that each reader requires book B, with probability pi, find the ordering of the books which minimizes P(Tk) for all k, where T is the (random) number of titles examined by a reader before discovery of the required book.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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It is required to place in order n books B₁, B2, ..., Bn on a library shelf in such a way that readers searching from left to right waste as little time as possible on average. Assuming that each reader requires book B₁ with probability pi, find the ordering of the books which minimizes P(Tk) for all k, where T is the (random) number of titles examined by a reader before discovery of the required book.
Transcribed Image Text:It is required to place in order n books B₁, B2, ..., Bn on a library shelf in such a way that readers searching from left to right waste as little time as possible on average. Assuming that each reader requires book B₁ with probability pi, find the ordering of the books which minimizes P(Tk) for all k, where T is the (random) number of titles examined by a reader before discovery of the required book.
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