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Q158Section III (Statistics)158 of 190

X1+X3X_1+X_3 and X1−X2X_1-X_2 are proportional, so their joint law is singular

Let (X1,X2)∼N2(μ,Σ)(X_1,X_2)\sim N_2(\mu,\Sigma) where Σ\Sigma is a positive definite matrix. Then which of the following has a singular normal distribution where X3=X1−2X2X_3=X_1-2X_2?

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