product of 2 normpdf is different to a bivariate mvnpdf with diagonal covariance matrix

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.

Answer 1

[David Goodmanson]

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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