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Independent normal random variables

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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?Y and variance ?σ?2Y of Y.

b) What is the distribution of Y?

c) Evaluate P(Y > ?σ? Y)

Reference no: EM132047883

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