An Engineering Editor for a Large Publishing Firm Is Trying

question 4

Essay

An engineering editor for a large publishing firm is trying to decide whether or not to publish a manuscript he
has received. In making a decision he feels that it is sufficient to imagine that there are just four states of nature
which are
• S1, the book will sell an average of 500 copies per year;
• S2, the average annual sales will be 1500 copies;
• S3, the average annual sales will be 3000 copies; and
• S4, the average annual sales will be 10,000 copies.
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The prior probabilities which he assigns to these states of nature are, respectively, 0.30, 0.40, 0.25, and 0.05. The
discounted profits if he publishes the book are projected to be, respectively, -$30,000, +$4,000, +$12,000, and
+$100,000. Of course, the discounted profit is $0 if he does not publish it.
To gain additional information, the publisher can send the manuscript to a reviewer who would say he likes the
manuscript. From previous experience with this reviewer, the publisher feels that the conditional probabilities
of the state of nature given this response from the reviewer are respectively 0.1, 0.3, 0.5, and 0.1. Should the
publisher publish the book? To answer this question, do the following:
(a) What is the prior optimal act? Draw your decision tree here.
(b) Calculate the EVPI before sending the manuscript out for review.
(c) What is the posterior optimal act? Draw the decision tree
(d) Calculate the EVSI.

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Definitions:

Glass Containers

Durable and recyclable vessels made of glass used to hold liquids and solids, often utilized for storage and packaging.

Upper Confidence Bound

The upper limit of a confidence interval, indicating the highest value that, with a certain level of confidence, is believed to encompass the true parameter.

Population Means

The averages of different populations, providing a measure of central tendency for each population's data.

Large Samples

Refers to datasets that are sufficiently large to enable statistically meaningful analysis, often used to achieve more accurate estimates of population parameters.