Consider a new model of linear regression:p(yx,w)=N(ywTx,f(x))

Where f(x)=x. Given a dataset of the form D={(xi,yi)}i=1N, derive the maximum likelihood estimator of w and the maximum a posteriori estimator of w assuming the prior p(w)=N(w0,2I).

Describe what effect this will have on the estimation of w and why. Finally, if you were fitting this model in practice, what, if any, practical or numerical concerns might you have separate from the usual concerns of linear regression?