Consider a binary hypothesis testing problem where under H the random variable X is Geometric with...

 

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Consider a binary hypothesis testing problem where under H₂ the random variable X is Geometric with expected value of 2, while under Ho, it is instead uniform (its pmf is constant) on the set of positive consecutive integers (2, 3, 4, 5). (a) Obtain the Maximum Likelihood rule. To be definite, ties are broken in favor of H₁. (b) Underthe Maximum Likelihood rule from part (a), obtain the probability of missed detection. (c) Let P(Ho) = p. For what value of p will Ho be always be chosen under MAP rule on the set of positive consecutive integers (2, 3, 4, 5}? Consider a binary hypothesis testing problem where under H₂ the random variable X is Geometric with expected value of 2, while under Ho, it is instead uniform (its pmf is constant) on the set of positive consecutive integers (2, 3, 4, 5). (a) Obtain the Maximum Likelihood rule. To be definite, ties are broken in favor of H₁. (b) Underthe Maximum Likelihood rule from part (a), obtain the probability of missed detection. (c) Let P(Ho) = p. For what value of p will Ho be always be chosen under MAP rule on the set of positive consecutive integers (2, 3, 4, 5}?

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aThe Maximum Likelihood rule would be to choose Hi if X2 and Ho otherwise This can be seen by noting ... View the full answer