% Rolling a pair of dice
% Textbook: Part I, "Discrete Random Variable", simulation exercise
%
% Each experiment is a pair of independent rolls. The 36 outcome pairs are
% equally likely, so every cell of the 6x6 table of relative frequencies
% approaches 1/36. As an example event, Pr(double six) = 1/36.

clearvars; close all
rng(0)

N = 1e5;                        % number of experiments
d = randi(6, [N 2]);            % column 1: first die, column 2: second die

% Relative frequency of each pair (i,j)
P = accumarray(d, 1, [6 6])/N;

figure
imagesc(P)
axis square
colorbar
xlabel('second die')
ylabel('first die')
title('Relative frequency of each pair, theory 1/36 = 0.0278')

fprintf('Pr(double six): theory = %.4f, simulation = %.4f\n', ...
    1/36, mean(d(:,1) == 6 & d(:,2) == 6))
fprintf('Pr(same face):  theory = %.4f, simulation = %.4f\n', ...
    1/6, mean(d(:,1) == d(:,2)))