Hi I would like to get connected with an expert who could take care of the course assignments for about two and a half months. Class only meet once a week.
Random Walk assignment MATH 210-01, Fall 2021 Ryan Pellico, Department of Mathematics, Trinity College In class we used two_d_walk_UDLR(num_steps) and two_d_walk_angle(num_steps) to perform “UDLR" and “angle" random walks of length num_steps. Both functions return the column vectors [x, y] of coondinates encourntered on the walk. Note that the lengths of x and y are num_steps + 1. The script visualize_walks performs each of the above random walks one time and plots the results in a figure using the plot() and scatter() functions. An example is shown below for num_steps = 10000. Additionally, we used the function distance_of_walkers(num_sims,num_steps) to repeatedly (num_sims times) run UDLR and angle walks of length num_steps and calculate the final distances from the starting point in the column vectors [distances_UDLR, distances_angle], each of which has length num_sims+1. Using the script distribution_of_distances(), we studied the distribution of distances for each type of random walk. An example is shown below for num_steps = 1000 and num_sims = 10000 1 1. (30 points) Create a new function three_d_walk(num_steps) that performs a 3-dimensional random walk of length num_steps, by starting at the origin (x, y, z) = (0, 0, 0) and rolling a fair 6- sided die to determine the direction of each step (up, down, left, right, front, back). The function should return the column vectors [x, y, z] which record the coordinates of each step of the walk. Hint: use the two_d_walk_UDLR(num_steps) function as a template. 2. (20 points) Create a new script visualize_3_d_walk that calls your function in 1. and uses the plot3() and scatter3() functions to visualize the results of a 3-dimensional walk of 10, 000 steps. Hint: use the visualize_walks script as a template. 3. (40 points) Write a script average_distance_plot that uses the distance_of_walkers() function to perform 10, 000UDLR and angle walks of length num_steps for each value of num_steps in the list 10:10:1000, and returns the average distance from the origin in column vectors averages_UDLR and averages_angle. Your script should also plot the resulting averages against the vector 10:10:1000 on the same axis. Use a red solid line with square markers for the UDLR averages, and a blue solid line with circle markers for the angle average. Include a legend, label your axes appropriately, and include a descriptive title. 4. (10 points) Using the graph in 3., hypothesize about the functional relationship between the number of steps in a walk and the average distance of the walker from the starting point. Does the relationship seem to depend on which type of walk (UDLR or angle) is performed? 2