Problem 6 1 Let X1, X2, X3 be three independent, identically distributed normal random variables with 50, 2 20 Let X X1 2X2 2X3 Compute (a) E(X) (b) V (X) (c) P( X 50 25) (d) The 90th percentile of the distribution of X

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Question: Problem 6.1 Let X1, X2, X3 be three independent, identically distributed normal random variables with = 50, 2 = 20. Let X = X1

Problem 6.1 Let X1, X2, X3 be three independent, identically distributed normal random variables with µ = 50, σ2 = 20. Let X = X1 − 2X2 + 2X3. Compute:

(a) E(X).

(b) V (X).

(c) P(| X − 50 |≤ 25).

(d) The 90th percentile of the distribution of X.

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