University of California Los Angeles Statistic Questions

Question Description

In the production of new microchips, 4% of parts appear defective. So, any part hasa prior probability of 0.04 to be defective. A certain voltage measurement is used toidentify the defects. For good parts, these measurements are normally distributedwith a mean of 4.5 V and a standard deviation of 0.2 V. For defective parts, thesemeasurements are normally distributed with a mean of 4.2 V and a standarddeviation of 0.2 V. A new part is tested, and the measured voltage is 4.3 V on it.

(a) Use discriminant analysis to classify this new part as either good or defective,if the penalty of any misclassification is the same.

(b) Suppose that it is ten times as harmful to label a defective part as a good partthan vice versa. That is, L(good | defective) = 10 L(defective | good). Howwill you classify the new part now?

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