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Q155Section III (Statistics)155 of 180

Multivariate normal — correlation between two linear combinations

Suppose X‾3×1∼MNormal3 ⁣(0‾,(20.520.510204))\underline X_{3\times1}\sim\text{MNormal}_3\!\left( \underline0,\left(\begin{smallmatrix}2&0.5&2\\0.5&1&0\\2&0&4 \end{smallmatrix}\right)\right). Then the correlation coefficient between X1−X3X_1-X_3 and 2X22X_2 is:

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