Centered random walk. A random sequence (So, S1, .. . ) is defined recursively by So = x0 and St = St-1 + Xt for t > 1, where No E R and X1, X2, ... are independent and identically distributed with a finite mean m. (a) Prove that the centered random walk defined by St = St -mt is a martingale with respect to information sequence (xo, X1, X2, . . .). (b) Is the centered random walk (St)tez, a martingale with respect to itself