If X1, X2, and X3 are independent random variables with E(X1) = 4, E(X2) = 3, E(

Question

If X1, X2, and X3 are independent random variables with E(X1) = 4, E(X2) = 3, E(X3) = 2, V(X1) = 1, V(X2) = 5, V(X3) = 2, and Y = 2X1 + X2 – 3X3,

(a) Determine E(Y) and V(Y).
(b) Assume X1, X2, and X3 are normal random variables. Compute the following probabilities: P(Y > 2.0) and P(1.3 Y 8.3).

If X1, X2, and X3 are independent random variables with E 4, EOK2 3, EOK3) E2, V(Xi) 3X3 Determine an (b) AssumeX1, X2, and X3 are normal random variables. Compute the following probabilities: POY 2.0 and P(1.3 Y S 8.3).

Explanation / Answer

ans=

a) E(Y) = E(2X1+X2-3X3) = 2 E(X1) + E(X2) - 3 E(X3) = 2 (4)+3-3(2) = 5
V(Y) = 2^2 V(X1) + V(X2) + (-3)^2 V(X3) = 4 (1)+(1)(5)+ 9 (2) = 27

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