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Jul 16 at 15:54 comment added unwissen @GrandesJorasses Sorry, this was just a typo which is now corrected. About your more specialised statement I would have to think first.
Jul 16 at 15:49 history edited unwissen CC BY-SA 4.0
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Jul 16 at 15:47 comment added Grandes Jorasses But the weights do not sum up to 1, or do I misunderstand something? So they are not conditional densities in the first place. In any case, I was indeed trying to work out the in which the $\beta$ coefficients lie in a bounded set. I think the statement is true if $XxY$ is a compact set in $\mathbb{R}^2$ by the uniqueness representation theorem of mixtures of normals. Thank you very much for your help in any case!
Jul 16 at 14:48 history answered unwissen CC BY-SA 4.0