In a certain factory, machines D, E and F all produce computer chips of the same type. Of their production, machines D, E and F, respectively produce 2%, 3% and 1% defective chips. Machine D produces 30% of the output of the factory, machine E 25% and machine F the rest. Suppose one chip is selected at random from the output of the factory and the chip is defective (a) Use Bayes' theorem to find the probabilities that the chip was manufactured on machines D, E and F. (b) Identify the data, hypotheses, likelihoods, prior probabilities and posterior proba- bilities. (c) Redo the computation of (a) using a Bayesian updating table.
In a certain factory, machines D, E and F all produce computer chips of the same type. Of their production, machines D, E and F, respectively produce 2%, 3% and 1% defective chips. Machine D produces 30% of the output of the factory, machine E 25% and machine F the rest. Suppose one chip is selected at random from the output of the factory and the chip is defective (a) Use Bayes' theorem to find the probabilities that the chip was manufactured on machines D, E and F. (b) Identify the data, hypotheses, likelihoods, prior probabilities and posterior proba- bilities. (c) Redo the computation of (a) using a Bayesian updating table.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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Transcribed Image Text:In a certain factory, machines D, E and F all produce computer chips of
the same type. Of their production, machines D, E and F, respectively produce 2%, 3%
and 1% defective chips. Machine D produces 30% of the output of the factory, machine
E 25% and machine F the rest.
Suppose one chip is selected at random from the output of the factory and the chip is
defective
(a) Use Bayes' theorem to find the probabilities that the chip was manufactured on
machines D, E and F.
(b) Identify the data, hypotheses, likelihoods, prior probabilities and posterior proba-
bilities.
(c) Redo the computation of (a) using a Bayesian updating table.
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VIEWStep 4: Redo the computation of (a) using a Bayesian updating table.
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