Question: Let y = XB + where y = [y1, ..., Un] and = = [=1, ..., En]] and X E Rnxd and B E Rd.

Let y = XB + where y = [y1, ..., Un] and = = [=1, ..., En]] and X E Rnxd and B E Rd. Assume that & ~ N(0, o'In) and consider Enew ~ N(0, 1). Assume further that & and Enew are independent. Let z E Rd be deterministic vector and set u(z) := 3 z where B = (XTX)-1Xy. (a) Find the joint distribution of [u(z), Enew] E R2. (b) Find the distribution of A(z) - Enew

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