Let 9 be a Bernoulli random variable that indicates which one of two hypotheses is true, and let P(9 = I) = 1). Under the hypothesis 8 = 0, the random variable X is uniformly distributor] over the interval [0, 1]. Under the alternative hypothesis 8 : 1, the PDF of X is given by 21:, if 0 <_: .1: g fx i _ otherwise. consider the map rule for deciding between two hypotheses given that x : assume now p is arbitrary such it turns out there exists a constant c always decides in favor of hypothesis if and only c. find>