The nomenclature in this article's title parallels the phrase law of total variance. Some writers on probability call this the "conditional covariance formula"[2] or use other names.
Note: The conditional expected values E( X | Z ) and E( Y | Z ) are random variables whose values depend on the value of Z. Note that the conditional expected value of X given the eventZ = z is a function of z. If we write E( X | Z = z) = g(z) then the random variable E( X | Z ) is g(Z). Similar comments apply to the conditional covariance.
↑ Matthew R. Rudary, On Predictive Linear Gaussian Models, ProQuest, 2009, page 121.
↑ Sheldon M. Ross, A First Course in Probability, sixth edition, Prentice Hall, 2002, page 392.
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