hw04 - For what values of π 1 π 2 and π 3 are the three...

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ENEE 324 ASSIGNMENT 4 Due Thu 09/17 A circuit is fabricated by one of three facilities, labeled i = 1 , 2 , 3. The fraction of circuits on the market produced by Facility i is π i . The table below shows the probabilities (likelihoods) that a circuit manufactured by each of the facilities has lifetime L less than 10,000 hours, between 10,000 and 20,000 hours, and longer than 20,000 hours. Facility L < 10,000 10,000 < L < 20,000 L > 20,000 1 0.5 0.3 0.2 2 0.4 0.4 0.2 3 0.1 0.3 0.6 A circuit is purchased, installed and operated until failure. (i) (5 pts.) Suppose the circuit lasts less than 10,000 hours. In terms of π i ’s, determine the posterior probabilities that the chip was manufactured by each of the three facilities. (ii) (2 pts.)
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Unformatted text preview: For what values of π 1 , π 2 and π 3 are the three posterior probabilities in part (i) equal? (iii) (5 pts.) Suppose the circuit lasts longer than 10,000 hours. Again, determine in terms of π i ’s the posterior probabilities that it was manufactured by each of the three facilities. (iv) (5 pts.) Suppose the circuit lasts longer than 20,000 hours. Determine in terms of π i ’s the posterior probability that it was not manufactured by Facility 1. (v) (3 pts.) If the posterior probability in part (iv) equals 0.1, what is the relationship between π 1 and π 2 ? What range of values of π 1 is consistent with that value (of 0.1)?...
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This note was uploaded on 03/21/2010 for the course ENEE 324 taught by Professor Ephrimedes during the Fall '05 term at Maryland.

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