%% Scripts used in class, MAT 331 August 28, 2018


%-----------------------------------------------
%  script to plot a one dimensional random walk
%  this walk steps -1,+1 with equal probability.

   N=1000;
   % make N-long vector of random -1 and +1's
   x=2*(randi(2,1,N)-1.5);
   % take cumulative sum
   y=cumsum(x);
   figure;
   hold on;
   grid on;
   plot(y,'r');
   title('A random walk')
   return;

%-----------------------------------------------
%  script to plot to compute where a random walk ends
%  this random walk steps -1,0,1 with equal probability

   trials=10000;
   N=1000;
   y=zeros(1,trials);
   for k=1:trials
      % make N-long vector of random -1 and +1's
      x=(randi(3,1,N)-2);
      y(k)=sum(x);
   end % for k
   figure;
   hold on;
   grid on;
   hist(y,100);
   title(['Histogram of ',num2str(trials),...
           ' random walks of length ',num2str(N)])
   return;