Use Matlab for the following problem

3. A lazy random walk is one that allows the particle to stay put instead of having to move left or right. For this situation, over a time-step of size t, assume the probability of going right a distance of x 1 is Pr-0.4 (from location x-l to z), the probability of going left a distance of -l is p-0.5 (frorn location x to x-1), and the probability of not moving is p.-0.1. Note that Pr + Pl + ps-1, where Pl0, pr0, and P. 0. (a) Simulate the trajectory of this particle over the time interval 0 t 100 using a time-step size of t = 1, Plot the location of the particle as a function of time corresponding to this particular realization of the particle trajectory. Also include a separate plot of another particle trajectory over the time interval 0 t 100 using a time-step size of t = 0.1. Compare the results of the two simulations in terms of the trajectory of the particle and its smoothness. 3. A lazy random walk is one that allows the particle to stay put instead of having to move left or right. For this situation, over a time-step of size t, assume the probability of going right a distance of x 1 is Pr-0.4 (from location x-l to z), the probability of going left a distance of -l is p-0.5 (frorn location x to x-1), and the probability of not moving is p.-0.1. Note that Pr + Pl + ps-1, where Pl0, pr0, and P. 0. (a) Simulate the trajectory of this particle over the time interval 0 t 100 using a time-step size of t = 1, Plot the location of the particle as a function of time corresponding to this particular realization of the particle trajectory. Also include a separate plot of another particle trajectory over the time interval 0 t 100 using a time-step size of t = 0.1. Compare the results of the two simulations in terms of the trajectory of the particle and its smoothness