(Weighted linear regression) In class when discussing linear regression, we assume that the Gaussian noise is independently identically distributed. Now we assume the noises 61,62, - - men are independent but each em m N (0, 0,21%), i.e., it has its own distinct variance. (a) Write down the log likelihood function of w. (b) Show that maximizing the log likelihood is equivalent to minimizing a weighted least square loss function J (W) = % 22:1 am (wam gm)2, and express each am in terms of am. (e) Derive a batch gradient descent algorithm for optimizing this objective. (cl) Derive a closed form solution to this optimization