Here's an example that you may be able to adapt to your problem.
Suppose [x1;x2] have a multivariate normal distribution with mean [2;3] and variance matrix [1 .6;.6 1]. Then we know theoretically that the marginal distribution of x1 is normal(2,1), the marginal distribution of x2 is normal(3,1), and the distribution of x2 conditional on x1 is normal with mean 3+.6*(x1-2) and standard deviation sqrt(1-.6^2). Let's see if we can verify that.
% Marginal distribution of x2 computed directly at four points
normpdf(1:4,3,1)
ans =
0.0540 0.2420 0.3989 0.2420
% Same computed by integrating the marginal of x1 and conditional of x2
for j=1:4
quad(@(x)normpdf(x,2,1).*normpdf(j,3+.6*(x-2),sqrt(1-.6^2)),-10,10)
end
ans =
0.0540
ans =
0.2420
ans =
0.3989
ans =
0.2420
