Let X 1 ,X 2 ,X 3 be a random sample from the normal distribution N(0, 2 ) Are the quadratic forms X 2 1 3X 1 X 2 X 2 2 X 1 X 3 X 2 3 and X 2 1 2X 1 X 2 2 3X 2 2 2X 1 X 2 X 2 3 independent or dependent

Question: Let X 1 ,X 2 ,X 3 be a random sample from the normal distribution N(0, 2 ). Are the quadratic forms X 2 1

Let X₁,X₂,X₃ be a random sample from the normal distribution N(0,σ²). Are the quadratic forms X²₁ +3X₁X₂+X²₂ +X₁X₃+X²₃ and X²₁−2X₁X₂+ 2/3X²₂ − 2X₁X₂ − X²₃ independent or dependent?

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