ndies = 20;
n = 100;
P = zeros(ndies, 6);
for i = 1:ndies
    % (a) roll a single die:
    x = rollthedie(n, 6);
    % (b) compute normalized histogram:
    [h,b] = hist(x, 1:6);
    h = h/sum(h);   % normalization
    % (c) store the histograms:
    P(i,:) = h;
end

% (c) mean and standard deviation for each eye:
m = mean(P, 1);
s = std(P, 1);

% (d) plot results:
bar(m, 'facecolor', [0.8 0 0]);   % darker red
hold on;
errorbar(m, s, '.k', 'linewidth', 2);   % k is black
set(gca, 'XTick', 1:6);
xlim([ 0, 7 ]);
ylim([ 0, 0.25])
xlabel('Eyes');
ylabel('Probability');
hold off;
savefigpdf(gcf, 'die2.pdf', 6, 5)