% TUAPPR file tuappr.m Discrete approximation to joint ac pair
% Version of 2/20/96
% Joint density entered as a function of t, u
% Sets up discrete approximations to X, Y, t, u, and density
rx = input('Enter matrix [a b] of X-range endpoints  ');
ry = input('Enter matrix [c d] of Y-range endpoints  ');
nx = input('Enter number of X approximation points  ');
ny = input('Enter number of Y approximation points  ');
dx = (rx(2) - rx(1))/nx;
dy = (ry(2) - ry(1))/ny;
X  = (rx(1):dx:rx(2)-dx) + dx/2;
Y  = (ry(1):dy:ry(2)-dy) + dy/2;
[t,u] = meshgrid(X,fliplr(Y));
P  = input('Enter expression for joint density  ');
P  = dx*dy*P;
P  = P/sum(sum(P));
PX = sum(P);
PY = fliplr(sum(P'));
disp('Use array operations on X, Y, PX, PY, t, u, and P')