1. Consider a 1D random walk involving steps with equal step lengths taken either in the positive or negative directions with probabilities p and q respectively. Follow the steps described below to compute the probability distribution P(x) for the net displacement z after N steps. (a) Write down and plot the single step probability density w(s) for this case. [2] (b) Compute Q(k) for the above w(s). [2] (c) Compute the expression for Q(k) N. [3] (d) Compute P(x) by taking the inverse Fourier transform of the answer above. [3]