Let θ be a bernoulli random variable that indicates which one of two hypotheses is true, and let θ=1)= . under the hypothesis θ=0 , the random variable has a normal distribution with mean 0 , and variance 1 . under the alternative hypothesis θ=1 , has a normal distribution with mean 2 and variance 1 . consider the map rule for deciding between the two hypotheses, given that = . suppose for this part of the problem that =2/3 . the map rule can choose in favor of the hypothesis θ=1 if and only if ≥ . find the value of .