(Answered) Consider 3 independent normal random variables x1 x2nbspand

Statistics

Consider 3 independent normal random variables X₁, X₂ and X₃, such that E[X₁] = 2, E[X₂] = 4, E[X₃] = 6, and V[X₁] = 3, V[X₂] = 5, V[X₃] = 7 Let Y be the following linear combination: Y = -3X₁ - X₂ +2X₃

a) Find the mean ?μ?_Yand variance ?σ?²_Y of Y.

b) What is the distribution of Y?

c) Evaluate P(Y > ?σ? _Y)

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