We talked about the robustness of Logistic Regression with respect to the distribution assumptions of features given the class labels. In this problem, we will consider two distributions from the exponential family and verify that they lead to a logistic posterior distribution:h θ (x)=P(y=1∣x;θ)=g(θ T x)= 1+e −θ T x 1​ .- Let,x∣y=1∼Poisson(λ 1 )and x∣y=0∼Poisson(λ 0). Show thatp(y=1∣x)is logistic. - Let,x∣y=1∼N(μ 1 ,σ 1 )andx∣y=0∼N(μ 0,σ 0). Show thatp(y=1∣x)is logistic. For both the above cases, you can assume that the two classes are equally likely to occur, i.e.,p(y=1)=p(y=0)andx is a real number (i.e., you have a one-dimensional feature).