% MS-A050x
% Example of a discrete joint distribution of two variables.
% (MATLAB/Octave code)
%
% X = #persons in household
% Y = #rooms in household
% P(X=x, Y=y) = proportion of such households

x = 1:6;
y = (1:6)';

pxy = [
    0.126	0.013	0.002	0.001	0.000	0.000
    0.196	0.086	0.012	0.005	0.001	0.000
    0.073	0.097	0.034	0.019	0.005	0.001
    0.038	0.079	0.031	0.030	0.010	0.003
    0.015	0.041	0.017	0.021	0.009	0.002
    0.004	0.012	0.006	0.007	0.003	0.001
    ];

% Marginal distribution of X, by taking column sums
px = sum(pxy, 1)

% Marginal distribution of Y, by taking row sums
py = sum(pxy, 2)

% Row of joint distribution, corresponding to Y=1 rooms and Y=6 rooms
pxrow1 = pxy(1,:)
pxrow6 = pxy(6,:)

% Conditional distributions, when Y=1 rooms and when Y=6 rooms
px_cond_y1 = pxrow1 / sum(pxrow1)
px_cond_y6 = pxrow6 / sum(pxrow6)

% Color picture of the bivariate distribution.
% Dark = large value.
imagesc(pxy); colormap(1-gray); colorbar; set(gca,'ydir','normal');
title('Finnish households')
xlabel('X = #persons')
ylabel('Y = #rooms')