Let θ be a bernoulli random variable that indicates which one of two hypotheses is true, and let p(θ=1)=p. under the hypothesis θ=0, the random variable x has a normal distribution with mean 0, and variance 1. under the alternative hypothesis θ=1, x has a normal distribution with mean 2 and variance 1.suppose for this part of the problem that p=2/3. the map rule can choose in favor of the hypothesis θ=1 if and only if x≥c1. find the value of c1.for this part, assume again that p=2/3. find the conditional probability of error for the map decision rule, given that the hypothesis θ=0 is true. p(error|θ=0)=find the overall (unconditional) probability of error associated with the map rule for p=1/2.