Suppose a particle is at the origin at time t=0. Consider the particle motion where it may move to the right with probability of 50% and to the left with a probability 50%. For time t, the random walk, x(t), may be described as the sequence x(0) = 0 x(t + 1) = x(t) 1 where movement at each step {-1, +1 is a random displacement to the left or right, respectively. For example, a random walk of 10 steps with x(0) 0 may be described using the sequence x = {0:-1; 0; 1; 2; 1; 2; 3; 4; 3; 2} a. Write a program in Matlab that simulates the particle trajectory using a random walk. For a specified t value (integer-valued), your program can either store the particle loca tion or the corresponding sequence of left/right steps and constructing the particle position at a later date (the second option has lower memory requirement) b. Plot 50 trajectories of 100 steps against time where time is on the x-axis and position, x(t), is on the y-axis. c. Calculate and plot the average position, (x(t)), at each time t of the 50 particles (initial value) Suppose a particle is at the origin at time t=0. Consider the particle motion where it may move to the right with probability of 50% and to the left with a probability 50%. For time t, the random walk, x(t), may be described as the sequence x(0) = 0 x(t + 1) = x(t) 1 where movement at each step {-1, +1 is a random displacement to the left or right, respectively. For example, a random walk of 10 steps with x(0) 0 may be described using the sequence x = {0:-1; 0; 1; 2; 1; 2; 3; 4; 3; 2} a. Write a program in Matlab that simulates the particle trajectory using a random walk. For a specified t value (integer-valued), your program can either store the particle loca tion or the corresponding sequence of left/right steps and constructing the particle position at a later date (the second option has lower memory requirement) b. Plot 50 trajectories of 100 steps against time where time is on the x-axis and position, x(t), is on the y-axis. c. Calculate and plot the average position, (x(t)), at each time t of the 50 particles (initial value)