Question: 4. [Alternative Risk Measure] Consider a binary hypothesis testing problem, where the goal is to minimize the following risk measure p(5) = [PF(8)]-+ PM(8) (a)

4. [Alternative Risk Measure] Consider a binary hypothesis testing problem, where the goal is to minimize the following risk measure p(5) = [PF(8)]-+ PM(8) (a) Show that the optimal solution is a (possibly randomized) likelihood-ratio test. (b) Find the optimal solution for the observation model Po(y) = 1 0 if y E [0, 1] otherwise and PI(y) = 2y if y E [0, 1] 0 otherwise

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