Using the notation from Example 2-38, what does the quantity, P(F'IS) mean? EXAMPLE 2-38 Bayesian Network Bayesian netwo

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Using The Notation From Example 2 38 What Does The Quantity P F Is Mean Example 2 38 Bayesian Network Bayesian Netwo 1 (115 KiB) Viewed 33 times

Using the notation from Example 2-38, what does the quantity, P(F'IS) mean? EXAMPLE 2-38 Bayesian Network Bayesian networks are used on the Web sites of high-technology manufacturers to allow customers to quickly diagnose problems with products. An oversimplified example is presented here. A printer manufacturer obtained the following probabilities from a database of test results. Printer failures are associated with three types of problems: hardware, software, and other (such as connectors), with probabilities 0.1, 0.6, and 0.3, respectively. The probability of a printer failure given a hardware problem is 0.9, given a software problem is 0.2, and given any other type of problem is 0.5. If a customer enters the manufacturer's Web site to diagnose a printer failure, what is the most likely cause of the problem? Let the events H, S, and O denote a hardware, software, or other problem, respectively, and let F denote a printer failure. The most likely cause of the problem is the one that corresponds to the largest of P(HIF), P(SIF), and P(OIF). In Bayes' Theorem the denominator is P(F) = P(FH)P(H) + P(FS)P(S) + P(F|O)P(O) = 0.9 (0.1) + 0.2(0.6) +0.5(0.3) = 0.36 Then, P(H|F)=P(FH)P(H)/P(F)=0.9(0.1)/0,36=0.250 P(SF)=P(FS)P(S)/P(F) = 0.2(0.6)/0.36=0.333 P(OF)=P(FO)P(O)/P(F)=0.5(0.3)/0.36=0.417 Notice that P(HIF) + P(S\F) + P(O|F) = 1 because one of the three types of problems is responsible for the failure. Because P(OIF) is largest, the most likely cause of the problem is in the other category. A Web site dialog to diagnose the problem quickly should start with a check into that type of problem. Practical Interpretation: Such networks are more commonly used to diagnose problems in areas as diverse as electronic products and healthcare. O The probability that there is a software problem if the printer is working. The probability that a printer works and the software works. O The probability that a printer works if it has software problem. O The probability that software works if it has a printer problem.