Compute and plot the path(s) of a set of random walkers which are confined by a pair of barriers at +B units and -B units from the origin (where the walkers all start from). A random walk is computed by repeatedly performing the calculation xj+1 = xj + s where s is a number drawn from the standard normal distribution (randn in MATLAB). For example, a walk of N steps would be handled by the code fragment x(1) = 0; for j = 1:N x(j+1) = x(j) + randn(1,1); end There are three possible ways that the walls can "act": a. Reflecting - In this case, when the new position is outside the walls, the walker is "bounced" back by the amount that it exceeded the barrier. That is, when xj+1 > B, xj+1 = B - |B - xj+1| when xj+1 < (-B), xj+1 = (-B) + |(-B) - xj+1| If you plot the paths, you should not see any positions that are beyond |B| units from the origin. b. Absorbing - In this case, if a walker hits or exceeds the wall positions, it "dies" or is absorbed and the walk ends. For this case, it is of interest to determine the mean lifetime of a walker (i.e., the mean and distribution of the number of steps the "average" walker will take before being absorbed). c. Partially absorbing - This case is a combination of the previous two cases. When a walker encounters a wall, "a coin is flipped" to see if the walker relfects or is absorbed. Assuming a probability p (0 < p < 1) for reflection, the pseudo-code fragment that follows uses the MATLAB uniform random-number generator to make the reflect/absorb decision: if rand < p reflect else absorb end What do you do with all the walks that you generate? Compute statistics, of course. Answering questions like What is the average position of the walkers as a function of time? What is the standard deviation of the position of the walkers as a function of time? Does the absorbing or reflecting character influence these summaries? For the absorbing/partial-reflection case, a plot of the number of surviving walkers as a function of step numbers is a very interesting thing.