final_practice_2009

# Final_practice_2009

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Unformatted text preview: ssed detection subject to the constraint that 0, otherwise the probability of false alarm PF A ≤ 1/4. 2y , 0 ≤ y ≤ 1 (c) Now suppose there is another hypothesis Hpy.H (Conditioned on H2 , the distribution of y is given by the 2 | y |H1 ) = 0, otherwise 2(1 − y ), 0 ≤ y ≤ 1 else p y |H2 ) decision rule. Compute the resulting probability of detection Specify(the MAP = 0 error. given graphically by (c) Now suppose there is another hypothesis, H2 . Conditioned on H2 , the distri(b) bution of y decision rule to minimize PM , subThatto the constraint that PF ≤ 1 . Specify the is given in the following ﬁgure ject is, 4 2 Py |H (y |H = 2) PSfrag replacements continued on the next page 1 4 0 yH Suppose that we can design a decision rule that can onlychoose),H0≤or≤ 1 1 (i.e. we are not allowed to choose H2 ) 2(1 − y py |H (y |H2)is = and suppose that the cost for deciding Hi when Hj true is Cij , with 0, otherwise C00 = C11 = 0, C01 = C10 = C02 = 1, C12 = 2 Suppose that we can design a decision rule that can only choose H0 or H1 (i.e., we are not allowed...
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## This note was uploaded on 01/08/2013 for the course ECE 531 taught by Professor Natasha during the Spring '10 term at Ill. Chicago.

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