JointDistCommands.m

%% generate the data

n = 1000; % which die was used first and second roll - fair, hi, lo dice1 = randi(3,[n,1]); dice2 = randi(3,[n,1]); % did the 'loading' happen for die 1 and die 2 load1 = randi(2,[n,1]); load2 = randi(2,[n,1]);

r1 = roll(dice1,load1,randi(5,[n,1]),randi(6,[n,1])); r2 = roll(dice2,load2,randi(5,[n,1]),randi(6,[n,1]));

D = [dice1,dice2,r1,r2];

%% There are lots of ways to visualize it

% show this as an image imagesc(D);

% sort and then show it as an image S = sortrows(D,1:2); imagesc(S);

% show a histogram D34 = D(:,3:4); hist3(D34,[6,6]);

% get the counts and 'centers' that define the histogram [H,C] = hist3(D34,[6,6]); P = H/1000; SP = (H + (1/36))/1001; [I,J]=meshgrid(1:6,1:6); surf(I,J,SP);

% we could also 'jitter' the points and do a scatter plot E = D34 + randn(1000,2)*0.1; plot(E(:,1),E(:,2),'r*');

% or combine that with a surface.... surf(I,J,SP); hold on; plot3(E(:,1),E(:,2),zeros(1000,1)+0.1,'r*');

%% Reasoning with the joint

% easy thing is to just look up interesting cases in the data and see how % frequent they are

sum(D(:,3)==D(:,4))/1000; % doubles sum(D(:,3)+D(:,4)==7)/1000; % sevens

% find all the indices of the data - in this case these are the different % outcomes of the joint experiment

[I,J]=find(SP); %all possible indices of SP IJ = [I,J]; %index 1,index 2

% then we can find where - at what indices - we get sevens or doubles conveniently... Sevens = IJ(I==J,:); Doubles = IJ(I==J,:);

sum(SP(sub2ind(size(SP),Sevens(:,1),Sevens(:,2)))); sum(SP(sub2ind(size(SP),Doubles(:,1),Doubles(:,2))));

% or even ask a hard question like: what is Pr(both die fair|roll>10)? fairAnd11Or12 = sum((D(:,1)==1) & (D(:,2)==1) & (D(:,3)+D(:,4) >= 10)); is11Or12 = sum((D(:,3)+D(:,4) >= 10)); fairAnd11Or12/is11Or12;