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Say we have two multivariate Gaussian random vectors $p(x_1) = N(0,\Sigma_1), p(x_2) = N(0,\Sigma_2)$, is there a well known result for the expectation of their product $E[x_1^Tx_2]$ E[x_1x_2^T]$ (matrix result) without assuming independence? Thanks. |
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Expectation of product of Gaussian random variablesvectorsSay we have two multivariate Gaussian random variables vectors $p(x_1) = N(0,\Sigma_1), p(x_2) = N(0,\Sigma_2)$, is there a well known result for the expectation of their product $E[x_1x_2]$ E[x_1^Tx_2]$ without assuming independence? Thanks. |
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Expectation of product of Gaussian random variablesSay we have two Gaussian random variables $p(x_1) = N(0,\Sigma_1), p(x_2) = N(0,\Sigma_2)$, is there a well known result for the expectation of their product $E[x_1x_2]$ without assuming independence? Thanks.
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