Covariance matrix for GMM

There is no way to answer this question?

even for writing the sample covariance matrix
formulation for the data set [X, Y] where
X(n observations) and Y (m observations) are from
the class 1 and class 2 which both are
multidimensional normal distribution?


----- Original Message -----
From: "Feng Zhang" <f0z6305 at labs.tamu.edu>
To: "R-Help" <r-help at stat.math.ethz.ch>
Sent: Tuesday, February 11, 2003 12:11 AM
Subject: [R] Covariance matrix for GMM

Hey, All

Now I generate a data vector X (d-dimension column vector) from a Gaussian
Mixture Model (GMM).
That is, the pdf of vector X is
f(X) = a1*N(u1, Cov1) + a2*(u2, Cov2)
where a1+a2 = 1, N is multidimensional normal distribution, ui is the mean
vecotr, Covi is the covariance matrix, i=1, 2.

So can I get the close forms of the mean and covariance matrix for the
random vector X?

Thanks very much.

Fred

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