Develop code as discussed in the section on Relationship between Number of Steps and Distance Covered to obtain a list of average distances covered for random walks of step sizes from 1 to 50. Then, using the data the program generates, do the analysis of Project 3.

Relationship between Number of Steps and Distance Covered

To discern a relationship between the number of steps, n, and average distance cov- ered in a random walk, we execute meanRandomWalkDistance(n, 100) for values of n from 1 to 50 and store each average distance in a list or array, listDist. Then, we employ the techniques of Module 8.3, Empirical Models, to determine the relationship.

function avgDist = meanRandomWalkDistance(n, numTests)

% RANDOMWALK Function to return average distance

% between first and last point in random walk of

% n steps, where the simulation is performed

% numTests number of times

sumDist = 0;

for j = 1:numTests

sumDist = sumDist + randomWalkDistance(n);

end;

function [dist] = randomWalkDistance(n)

% RANDOMWALKPOINTS Function to produce a random walk, where at each time

% step the entity goes diagonally in a NE, NW, SE, or SW direction, and to

% return a list of the points in the walk

% Pre: n is the number of steps in the walk.

% Post: The distance from the starting point has been returned.

x = 0;

y = 0;

lst = zeros(n + 1,2);

lst(1, :) = [0 0];

for i = 1:n

if randi([0,1]) == 0

x = x + 1;

else

x = x - 1;

end;

if randi([0,1]) == 0

y = y + 1;

else

y = y - 1;

end;

lst(i + 1, :) = [x y];

end;

dist = sqrt(x^2 + y^2);

avgDist = sumDist/numTests;

%listDist = append(avgDist);