5.6.1 X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following: a. E(3X+2Y) c. P(3X + 2Y < 18) b. V(3X+2Y) d. P(3X + 2Y < 28)

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5.6.1 X and Y are independent, normal random variables with
E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.
Determine the following:
a. E(3X+2Y)
c. P(3X + 2Y < 18)
b. V(3X+2Y)
d. P(3X + 2Y < 28)
Transcribed Image Text:5.6.1 X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following: a. E(3X+2Y) c. P(3X + 2Y < 18) b. V(3X+2Y) d. P(3X + 2Y < 28)
Expert Solution
Step 1: We have given that

E(X)=2, V(X)=5, E(Y)=6, V(Y)=8

X and Y are independent then Cov(X,Y)=0

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