Question

Let Î be a Bernoulli random variable that indicates which one of two hypotheses is true, and let P(Î = 1) = p. Under the hypothesis Î = 0, the random variable X is uniformly distributed over the interval [0,1]. Under the alternative hypothesis Î = 1, the PDF of X is given by fX| Î(x|1) = 2x if 0<=x<=1 and 0 otherwise. Consider the MAP rule for deciding between the two hypotheses, given that X=x. Find the probability of error associated with the MAP rule as a function of p.

Answer 1

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