I know that the difference of two multivariate or univariate normally distributed random variables produces another (multivariate) normal random variable. But, what happens when you take the difference of multivariate random variables each with different numbers of variables. For example, what happens when you take the difference of a normally distributed bivariate normal random variable and a univariate normally distributed random variable?

See http://mathworld.wolfram.com/NormalDifferenceDistribution.html

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    $\begingroup$ What might $(2,3)-4$ mean? Is it even a sensible question? $\endgroup$ – Henry Dec 17 '15 at 19:03

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