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EECE5612.MERGED.202530 quiz 2
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Random variable Y is known to be exponentially distributed, either with the average rate λ0=1 (hypothesis H0) or with the average rate λ1=λ0/10 (hypothesis H1). A decision H0/H1 has to be made based on a single observation y of Y. The cost of missed detection, Cmd=C01 is ten times the cost of false alarm Cfa=C10=10 thousand dollars. Correct decisions cost nothing. If it is known that P1=0.1, specify the Bayesian decision rule that will minimize the average cost. What is the resulting average cost? Mark the correct answer (numbers are rounded):
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We are given a single observation y from Y, with Y ~ Exp(lambda) where lambda is either lambda0 = 1 under H0, or lambda1 = lambda0/10 = 0.1 under H1. The prior is P1 = 0.1 for H1 and P0 = 0.9 for H0. Costs: C10 (false alarm: decide H1 when H0 is true) = 10 thousand dollars, and C01 (missed detection: decide H0 when H1 is true) = Cmd = 10 times C10 = 100 thousand dol......Login to view full explanationLog in for full answers
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