Please answer both question (a) (b) (c) (d) in this problem

3. (20 points) Consider the elementary process defined as follows: -1, if 0 St B.(w) 5.w= -2, if 2 st 6. (a) Compute E[S52dt) . Hint: {E,} has two possible sample paths, each of which is a step function. (b) Compute Var(S_5_dB.). (C) Simulate paths of {B} and compute the corresponding paths of the stochastic integral over the interval (0,7). Plot them side by side. (Plot two, one for each case.) (d) Sample 10000 Brownian paths. For each path, compute 17 = S5dB. Plot the density estimate of 1,. Is I, normally distributed? 3. (20 points) Consider the elementary process defined as follows: -1, if 0 St B.(w) 5.w= -2, if 2 st 6. (a) Compute E[S52dt) . Hint: {E,} has two possible sample paths, each of which is a step function. (b) Compute Var(S_5_dB.). (C) Simulate paths of {B} and compute the corresponding paths of the stochastic integral over the interval (0,7). Plot them side by side. (Plot two, one for each case.) (d) Sample 10000 Brownian paths. For each path, compute 17 = S5dB. Plot the density estimate of 1,. Is I, normally distributed