Consider a two hypothesis decision problem where (a) Find the likelihood ratio Icirc (Z) (b) Letting the threshold n be arbitrary, find the decision regions R 1 and R 2 illustrated in Figure 11 1 Note that both R 1 and R 2 cannot be connected regions for this problem that is, one of them will involve a multiplicity of line segments Figure 11 1 (i ) and fz(z H2) exp exp( z ) fz(z Hj) 2 f,(z H ) f,(z H,) R1 R2 R1 R2 0 k

Question: Consider a two-hypothesis decision problem where (a) Find the likelihood ratio Î(Z). (b) Letting the threshold n be arbitrary, find the decision regions R 1

Consider a two-hypothesis decision problem where
(зi-) and fz(z|H2) exp = ; exp(-|z|) fz(z|Hj) = 2л

(a) Find the likelihood ratio Î›(Z).

(b) Letting the threshold n be arbitrary, find the decision regions R₁ and R₂ illustrated in Figure 11.1. Note that both R₁ and R₂ cannot be connected regions for this problem; that is, one of them will involve a multiplicity of line segments.

Figure 11.1

$f,(z|H}) f,(z\H,) R1 -R2 -R1 R2 0| k$

(i-) and fz(z|H2) exp = ; exp(-|z|) fz(z|Hj) = 2 f,(z|H}) f,(z\H,) R1 -R2 -R1 R2 0| k

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