Generate a random walk using a binomial process with p = 0.5. Assume that at each step the random walk takes on values 1 (with probability p), and −1 (with probability 1 − p). Perform
1000 random walk steps and calculate expected value and variance of a step of the random walk. Calculate the sum of the random walk over all 1000 steps. Repeat 500 times and compute the mean and variance of the random walk.