Editing Multivariate random variable (section)

===Expectation of the product of two different quadratic forms===
One can take the expectation of the product of two different quadratic forms in a zero-mean [[Joint normality|Gaussian]] random vector <math>\mathbf{X}</math> as follows:<ref name=Kendrick/>{{rp|pp. 162–176}}

:<math>\operatorname{E}\left[(\mathbf{X}^{T}A\mathbf{X})(\mathbf{X}^{T}B\mathbf{X})\right] = 2\operatorname{tr}(A K_{\mathbf{X}\mathbf{X}} B K_{\mathbf{X}\mathbf{X}}) + \operatorname{tr}(A K_{\mathbf{X}\mathbf{X}})\operatorname{tr}(B K_{\mathbf{X}\mathbf{X}})</math>

where again <math>K_{\mathbf{X}\mathbf{X}}</math> is the covariance matrix of <math>\mathbf{X}</math>. Again, since both quadratic forms are scalars and hence their product is a scalar, the expectation of their product is also a scalar.