Please help me to solve this question as below. Regression and Classification.

The standard linear regression model is: y = Xw te, where X is an n x d matrix of predictor vari- ables, y is an n-dimensional vector of response variables, and e ~ N(0, o'I) is an n-dimensional vector of model errors. (a) What is the PDF of y in terms of X, w, o2? (b) Let the PDF from part (a) be denoted as f(y|w). Suppose also in this case that w ~ N(0, p2I). Write an expression for the joint PDF of w and y (e.g. f(w, y)). (c) Show that WMAP = arg min 1/w/ /2 + lly - Xw| |2 (1) W 02 02