Problem 8.3 (Random walk with drift, 35pts ). Consider a one-dimensional random walk where the probability of stepping rightward is . If =1/2, the random walk is said to be biased. Consider a random walk of N steps of length , each of which takes time . a) Show that the mean displacement x=Nb, where b=21 is the directional bias of the talk (1b1). b) Show that the variance of the displacement (xx)2=N(1b2)2