terminology - Differences between variable and variate - Mathematics . . . 13 From Wikipedia A random variate is a particular outcome of a random variable If I understand correctly, a random variable is a measurable mapping, and a random variate is just a member of the codomain of a random variable In general, what differences are between variable and variate in mathematics? What do they mean respectively? Thanks!
composition method of generating random variables It does, actually If you understand how to generate the random variates using the other methods, then the straightforward algorithm that you have posted tells you exactly how to generate a random variate using this method
Multivariate control variate technique - Mathematics Stack Exchange When there is only one control variate, the Linear Least Squares approach reduces to the closed form formula you showed It is also possible, though less commonly used, for control variates to appear (be used) nonlinearly In that case, Nonlinear Least Squares can be used to determine the optimal parameters
Moment generating function for multivariate normal One definition of a multivariate normal vector $X$ is that any linear combination $t^\top X$ is univariate normal Using MGF of univariate normal the calculation can
Exponential family representation of multi-variate Gaussians I'm a bit stumped by the exponential family representation of a multi-variate Gaussian distribution Basically, the exponential form is a generic form for a large class of probability distributions