% Rolling of a fair die
% Proportion of 6's in N rolls. N rolls repeated M times
% Plot:  Histogram of the proportion with 
%       superimposed theoretical probability of 1/6.
clear all
close all

  disp('Proportion of Sixes')
  lw = 2; 
  set(0, 'DefaultAxesFontSize', 16);
  fs = 15;
  msize = 10;
%





M=1000; %M is number of different simulations
N=1000; %N is number of rolls in a single simulation
psixs =[]; %Keep here the proportion of 6's.
for i = 1:M
    nsix=0;
    for j= 1:N
         nsix = nsix + (rand<1/6);
    end
   psix = nsix/N;
   psixs = [psixs psix]; %collect all approximate probabilities
end
hist(psixs, 20)
hold on
plot([1/6 1/6],[0 N/5],'r-', 'linewidth',4)
hold off
mean(psixs)