3. Let G be a Bernoulli random variable that indicates which one of two hypotheses is true, and let P{8 : l) : p. Under the hypothesis 9 : 0, the random variable X is uniformly distributed over the interval {0,1}. Under the alternative hypothesis 8 = l, the PDF of X is given by 2.1:, if 0 E I g 1, fX|8($ I 1) _ { 0, otherwise. Consider the MAP rule for deciding between the two hypotheses, given that X : 1:. (a) Suppose for this part of the problem that p = 3/ 5. The MAP rule can choose in favor of the hypothesis 8 : 1 if and only if a: 2 (:1. Find the value of (:1. (b) Assume now that p is arbitrary such that 0 S p g 1. It turns out that there exists a constant (3 such that the MAP rule always decides in favor of the hypothesis 8 = 0 if and only if p