% begin definitions and initialisation

T = 500; % define running time T
N = 10; % define number of realisations N
X = zeros(N,T); % pre-allocate array to store realisations
% Should have N rows of length T
% i.e. X(2,3) should give value of realisation 2 at time 3
t = [1:T]; % create integer array of times
X(:,1) = 0; % initial position is always zero

% end initialisation
% begin simulation

for j =1:N % begin loop over realisations
    for i=1:T-1 % begin loop through timesteps
        r = rand(); % create random variable
        if r < 0.8;
            X(j,i+1) = X(j,i); % next position is the same
        elseif r < 0.9
            X(j,i+1) = X(j,i) - 1; % next position is back
        else
            X(j,i+1) = X(j,i) + 1; % next position is forward
        end
    end % end loop through timesteps
end % end loop over realisations

% end simulation

% begin plotting

% there are many nice ways to produce handsome plots in MATLAB
% shown here are just my personal preferences

figure('Color',[1 1 1]); % create figure with white background
set(gca,'FontSize',20) % set fontsize for axes
plot(X','LineWidth',2) % plot data N.B. Transpose required to plot X vs T
hold on; % hold the plot
grid on; % plot gridlines (looks nice)
plot(t,sqrt(t),'k',t,-sqrt(t),'k','LineWidth',2) % plot variance
axis([0,T,-1*T/20,+1*T/20]) % x-axis between 0 and T
% N.B. limits of y-axis have been 'fudged' a bit here...

xlabel('Time t','FontSize',20);ylabel('Position x','FontSize',20);

% N.B. plotting the character string 'LineWidth' followed by a 2
% makes the plot look a little nicer (in my view) and easier to read,
% however your mileage may vary.

% end plotting