Thus for network a f f1 f2 by the assumption that f1

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Unformatted text preview: atrix. The larger number in each column is underlined.) (d) For the MAP rule, pfalse alarm = P [(X, Y ) ∈ {(1, 2), (2, 2)}|H0 ] = 0.01 + 0.01 = 0.02, and pmiss = P ((X, Y ) ∈ {(1, 2), (2, 2)}|H1 ) = 1 − P ((X, Y ) ∈ {(1, 2), (2, 2)}|H1 ) = 1 − 0.24 − 0.48 = 0.28. Thus, for the MAP rule, pe = (0.8)(0.02) + (0.2)(0.28) = 0.072. (This pe is also the sum of the probabilities in the joint probability matrix that are not underlined.) (e) Using the conditional probabilities found in (a) and the given values of π0 and π1 yields that for the ML rule: pe = (0.8)(0.14) + (0.2)(0.11) = 0.134, which is larger than the value 0.072 for the MAP rule, as expected because of the optimality of the MAP rule for the given priors. 2.12. RELIABILITY 2.12 61 Reliability Reliability of complex systems is of central importance to many engineering design problems. Extensive terminology, models, and graphical representations have been developed within many different fields of engineering, from construction of major structures to logistics...
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