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Probability of a specific type of sample

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Probability of a specific type of sample

Hi! My question is: There’re two multivariate gaussian distrubution with different means/location factors, their images are in the same RnsuperscriptRnR^{{n}}. Then we withdraw samples from these two variables at random (the weights are random variables).

Given a point in this sample, it may come from the sample of the first variable, or from the sample of the second variable. Or it may also happen that this point (this vector) ”occurs”/takes place in both samples. Given XXX, a (compact) region in RnsuperscriptRnR^{{n}}, may the probability of this point belonging to this region XXX be formalized as : P(X)=Px1(X)+Px2(X)+Px1,x2(X)PXsubscriptPx1XsubscriptPx2XsubscriptPx1x2XP(X)=P_{{x1}}(X)+P_{{x2}}(X)+P_{{x1,x2}}(X) ? Thanks


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