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I think you mean product. The sum of two Gaussians isn't a Gaussian.
by montecarl 14y ago
I think you mean product. The sum of two Gaussians isn't a Gaussian.
- yummyfajitas 14y agoI think he meant the sum of two gaussian random variables is a gaussian. I.e., if X and Y are both drawn from a gaussian distribution, then X+Y is too.
- mturmon 14y agoRight. (You also need X and Y to be independent, or at least multivariate Gaussian -- i.e., X and Y can both be Gaussian but (X,Y) can fail to be Gaussian as a pair.) The product of Gaussian random variables is certainly not Gaussian.
- Evbn 14y agoWhen thinking about monoids, the word sum and product aren't distinguishable unless you specific the precise operation, as neither one is a canonical analogy to integer sum/product. Pointwise combination is an unattractive definition, as it ignores a lot of interesting structure in a connected space like real numbers. Indeed, convolution, the common way of combining functions, is defined as a sum of products at each point.