Consider the case of the random walk problem with equal probability of taking steps of length / to the left or right. (a) For the 1-D problem give an expression for the exact probability that after N steps one will be (i) back at the origin (ii) at a distance nl from the origin. assuming that N and n are even. (b) For the problem in part (a) give approximate numerical values for part (i) for the explicit case of N = 70 and for part (ii) for the case of N = 70 and n = 20. (c) In lecture we showed that for one dimension (1-D), and with equal left and right probability, the rms deviation from the origin after N steps of length is N. Find the rms deviation for the random walk in 2-D and 3-D assuming each step must be along one of 2 or 3 orthogonal directions respectively.