MATLAB: Product of 2 normpdf is different to a bivariate mvnpdf with diagonal covariance matrix

mvnpdfnormpdf

I expect that the bivariate normal probability density function of two variables that are not correlated (i.e. I use a diagonal covariance matrix) should be the same as the product of two univariate normal probability density functions. To be more specific I would expect that F1 is equal to F2, but it is not
F1 = mvnpdf([10 10],[15 5],[1 2]);
F2 = normpdf(10,15,1)*normpdf(10,5,2);
I would greatly appreciate any help on whether I am missing something.
Thank you very much in advance.

Best Answer

Hi A,
cov is specified by the covariance matrix, which in the diagonal case is simply independent variances. normpdf is specified by standard deviation. Try
F1 = mvnpdf([10 10],[15 5],[1 2])
F2 = normpdf(10,15,sqrt(1))*normpdf(10,5,sqrt(2))
F1 = 8.0962e-10
F2 = 8.0962e-10
>>
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