Prashant Kumar answered . 2024-04-21 08:30:23

fill([0 0 1],[0 1 0],'r')
axis equal

abc = randfixedsum(3,10,1,0,1);
sum(abc,1)
ans =
   1  1  1  1  1  1  1  1  1  1

a = abc(1,:);
b = abc(2,:);

It will always be true that a+b<=1. The variable c=1-a-b will have the same distribution as a and b. And the three variables together will be uniformly distributed.

abc = randfixedsum(3,10000,1,0,1);
plot3(abc(1,:),abc(2,:),abc(3,:),'.')
grid on
box on
axis equal

abc = randfixedsum(3,10000000,1,0,1);
hist(abc(1,:),1000)

ab = rand(1e6,2); ab(sum(ab,2) > 1,:) = []; size(ab) ans = 500444 2

So we rejected roughly 50% of the samples, as expected

subplot(3,1,1)
hist(ab(:,1),1000)
subplot(3,1,2)
hist(ab(:,2),1000)
subplot(3,1,3)
hist(1-sum(ab,2),1000)

mean([ab,1-sum(ab,2)],1)
ans =
      0.33328       0.3334      0.33332

std([ab,1-sum(ab,2)])
ans =
      0.23575      0.23549      0.23556

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