Consider a particle, which can start at x = 0 and move a distance Ax in either direction along the x-axis in a time At. If each displacement Xi takes one of the two possibilities (+4x, each with 1-Ax' equal probability, and that the X, are stochastically independent, 1. What is the net displacement after n steps, i.e., after time n At? 2. What is the mean displacement? 3. What is the variance for each X? 4. Prove that the variance of the net displacement is (X)_ (4x) L At