Let a = 0.1, b = 0.01, sigma = 0.5, T = 2, X_0 = 0.02. Write Matlab codes for the following two questions: a) Solve the SDE (1) using the Milstein scheme. Plot the numerical solution together with one sample path of (2). Add an appropriate legend. Print out the plot. b) Solve the SDE (1) using the Euler-Maruyama scheme to generate 500 sample paths and plot the first five sample paths. In the same figure, plot the average of the 500 sample paths, as well as the expectation function E(X_t) derived previously. Add an appropriate legend. Print out the plot. Let a = 0.1, b = 0.01, sigma = 0.5, T = 2, X_0 = 0.02. Write Matlab codes for the following two questions: a) Solve the SDE (1) using the Milstein scheme. Plot the numerical solution together with one sample path of (2). Add an appropriate legend. Print out the plot. b) Solve the SDE (1) using the Euler-Maruyama scheme to generate 500 sample paths and plot the first five sample paths. In the same figure, plot the average of the 500 sample paths, as well as the expectation function E(X_t) derived previously. Add an appropriate legend. Print out the plot