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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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.
 Spring '08
 Zahrn
 The Land

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