Question: The conditional pdfs corresponding to two hypotheses are given: f(y|H0) = 1/2 exp(-y/2), y>0 f(y|H1) = 1/4 exp(-y/4), y>0 Suppose we want to test these

The conditional pdfs corresponding to two hypotheses are given:

f(y|H0) = 1/2 exp(-y/2), y>0

f(y|H1) = 1/4 exp(-y/4), y>0

Suppose we want to test these hypotheses based on two independent samples y1 and y2. Assume equally likely priors.

a) Derive the Bayes decision rule for the test, assuming C00 = C11 = 0 and C01=C10 = 1.

b) Calculate Pr(D0 | H1) and Pr(D1 | H0)

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