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I have two 2x2 covariance matrices, stemming from bivariate datasets that are approximately normally distributed. I want to create a mixture distribution and for that I need to merge the covariance matrices. To find the variances, can I apply the following formula? Var(X) =$\Sigma_{i=1}^k\pi_i \sigma_i^2+\Sigma_{i=1}^k \pi_i(\mu_i-\mu)^2$ with $\pi_i$ being the mixture weights.

But how do I mix the covariances?

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  • $\begingroup$ Could you explain how "merging" the covariances will help you create a mixture distribution? $\endgroup$ – whuber Sep 6 '13 at 18:34

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