Making relative histogram for data, and a convergence diagram to see if enough trials have been run for monte carlo simulation.

I have written a monte carlo code for a double dice throw that calculates the probability of the throw sum being 8 or over 8. I have to make a relative frequency histogram for the sum of the dice with 11 bins. And show a convergence diagram to show that enough trials have been done. I do not know which part of my code to plot into the histogram to make a relative frequency histogram. I also do not know how to make a convergence diagram to show enough trials were done.

count = 0;
for i=1:1000;
  throwD1  = randi(6, 1);
  throwD2  = randi(6, 1);
  Throwsum = throwD1 + throwD2;  
  if Throwsum >=8
    fprintf('Sum>=8');
    count = count + 1;
  else
    fprintf('Sum<8');
  end
end
fprintf('Number of throws with sum=7: %d\n', count);
nAllruns = 0;
n8   = 0;
for throwD1 = 1:6
    for throwD2 = 1:6
        nAllruns = nAllruns + 1;
        if throwD1 + throwD2 >= 8
            n8 = n8 + 1;
        end
    end
end
prob=n8 / nAllruns

Answer 1

[Alan Stevens]

Something like the following?

N = 1000;
Throwsum = zeros(N,1);
Relativefreq = zeros(N,1);
count = 0;
for i=1:1000
  throwD1  = randi(6, 1);
  throwD2  = randi(6, 1);
  Throwsum(i) = throwD1 + throwD2;  
  if Throwsum(i) >=8
    count = count + 1;
  end
  Relativefreq(i) = count/i;
end
figure
histogram(Throwsum,11);
xlabel('Sum of two dice'), ylabel('Frequency')

figure
plot(1:N,Relativefreq),grid
xlabel('trials'),ylabel('Prob sum >= 8')

fprintf('Relative number of throws with sum >= 8: %d\n', count/N);

Relative number of throws with sum >= 8: 4.110000e-01