Recall that {x,} is a martingale if E [xn+h Ix\" ,x,,_1, ' ' ' ]=xn for all n and for all lead times it >0. Actually, to establish that {x,} is a martingale, one simply needs to prove the above formula for k =1 since it can be shown that if it holds for h =1 it must hold for all h >0. 1) Suppose x, =x,_1+, where 3, =8, +Be,_le,_2, Bio, and {(3,} is strict white noise. a) What is the best linear predictor of xn+1 based on x" ,x_1 , - - - ? Justify your answer. b) What is the best possible predictor of xn+1 based on x,, ,xn_1, - ' - ? Justify your answer. c) Compare your answers to a) and b) to decide whether {x1} is a martingale. (Keep in mind the discussion at the top of this handout)