Hi David
From what I understand, you are trying to recreate the probability density function fy(y) from the joint distribution probability function f(x,y) and want to compare its standard deviation sig3 with sig0.
According to probability theory, the way to obtain the probability denitrify function fy(y) from the joint distribution probability density function f(x,y) is to integrate f(x,y) with respect to x from –inf to inf.
However, the midline F(31,:) gives you the output of the function f(0,y) which is not related to a density function.
To recreate the 1-D distribution, please use the pair (x2, sum(F,2)) instead of (x2, F(31,:)). That is to say, the line
y2 = F(31,:)
should be replaced with
y2 = sum(F,2)/10;
Notice that this is a quadrature approximation of the integral, as pointed out by John D'Errico in his comment below. But it should be enough for you to test if the way you use the function mvnpdf is correct or not. Also, even without being divided by the factor 10, y2 could still be used to give the same answer since the function gaussfit takes care of the normalization. (Assuming gaussfit is the one you found in FileExchange via the link http://www.mathworks.com/matlabcentral/fileexchange/35122-gaussian-fit )
I have tested the revised code, and found that sig3 = sig0, which seems to be what you expected.
-Yu
