题目
题目

EECE5612.MERGED.202530 midterm part 1

数值题

Consider Question (6) again, but this time take into consideration the fact that the manufacturer offers a partial refund of $125 for all computers that are found to be faulty due to factory error. In order to get the refund, you must ship the broken computer back to the manufacturer, who will then run diagnostics to determine if the computer was among the faulty ones (and not broken due to an unrelated reason). Shipping costs $50. If the manufacturer establishes that the computer was faulty due to the manufacturing error, a refund of $125 will be issued to you (no extra compensation for shipping). If you ship the computer and it turns out not to be faulty, no refund will be issued (you will have wasted $50). Set up a Bayesian decision rule for this case. Show that it reduces to comparing the observation (11 months) to a threshold. Express the threshold in months, and and write the result, rounded to the nearest integer, in the space provided below.

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思路分析
The problem asks to set up a Bayesian decision rule for whether to ship the broken computer to the manufacturer in order to possibly receive a $125 refund, given a $50 shipping cost, and then to show that the decision reduces to comparing the observed age (11 months) to a threshold expressed in months, with the final threshold given as 14 months. First, restate the scenario clearly: you incur a shipping cost of $50 whenever you ship the computer. If the manufacturer confirms the fault is due to factory error, you receive a refund of $125. If the computer is not faulty, you get no refund and you do not recoup the shipping cost. Therefore, shipping is a decision that has a nonzero chance of a net gain (if faulty) or a net loss (if not faulty). Next, set up the Bayesian decision rule conceptually. Let F denote the event that the computer is faulty due to manufacturing error, and let X be the observed informatio......Login to view full explanation

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