32. The intensity of light reflected by an object is measured. Suppose there are two types of possible objects, A and B. If the object is of type A, the measurement is normally distributed with mean 100 and standard deviation 25; if it is of type B, the measurement is normally distributed with mean 125 and standard deviation 25. A single measurement is taken with the value X 120. a. What is the likelihood ratio? b. If the prior probabilities of A and B are equal ( each), what is the posterior probability that the item is of type B? c. Suppose that a decision rule has been formulated that declares the object to be of type B if X > 125. What is the significance level associated with this rule?
32. The intensity of light reflected by an object is measured. Suppose there are two types of possible objects, A and B. If the object is of type A, the measurement is normally distributed with mean 100 and standard deviation 25; if it is of type B, the measurement is normally distributed with mean 125 and standard deviation 25. A single measurement is taken with the value X 120. a. What is the likelihood ratio? b. If the prior probabilities of A and B are equal ( each), what is the posterior probability that the item is of type B? c. Suppose that a decision rule has been formulated that declares the object to be of type B if X > 125. What is the significance level associated with this rule?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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