Question 6 It is a standard result, which you may assume, that if X₁ and X₂ are independent and normally distributed random variables, then X₁ + X₂ is normally distributed. Suppose X₁,..., Xn are independent normal random variables, X; having mean µį and vari- ance of. If a₁,..., an are constants, show that Σ₁a;X; is normally distributed and find its mean and variance.

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