Question 3 {a} [15 marks] For a given loss function L, an optimal forecast is obtained by minimising the conditional expectation of the future loss, conditional on the information available: to\" a argmgn E [L (to, an IE] Given the quadratic loss function L[y.l 3}} = (y - 33:91 Show that the optimal forecast is the conditional mean. [b] [15 marks] Consider another quadratic loss flmction, L'fy, Q} = o+h[y - 1}}2. Derive the optimal forecast in this case and discuss the effect of taking a linear transformation of the meansquareerror loss function on the optimal forecast