Refer to Exercise 6.36. (a) Show that (2 X_{1}-X_{2}-4 X_{3}-12) has a normal distribution. (b) Find the

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Refer to Exercise 6.36.

(a) Show that $2 X_{1}-X_{2}-4 X_{3}-12$ has a normal distribution.

(b) Find the mean and variance of the random variable in part (a).

Data From Exercise 6.36

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Probability And Statistics For Engineers

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9th Global Edition

Authors: Richard Johnson, Irwin Miller, John Freund

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Refer to Exercise 6.36. (a) Show that (2 X_{1}-X_{2}-4 X_{3}-12) has a normal distribution. (b) Find the

Question:

6.36 Let X1, X2, and X3 be independent normal variables with E(X1)= 5 and = 9 E(X2)=-2 and = 2.25 E(X3) = 5 and = 4 (a) Show that 2X1 +2X2 +5X3 has a normal distri- bution. (b) Find the mean and the variance of the random vari- able in part (a).

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Probability And Statistics For Engineers

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