Let (X) and (Y) be independent normal random variables with [begin{array}{lll}E(X)=4 & text { and } &

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Let $X$ and $Y$ be independent normal random variables with

\[\begin{array}{lll}E(X)=4 & \text { and } & \sigma_{X}^{2}=25 \\E(Y)=3 & \text { and } & \sigma_{Y}^{2}=16\end{array}\]

(a) Use moment generating functions to show that $5 X-4 Y+7$ has a normal distribution.

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

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Probability And Statistics For Engineers

ISBN: 9780134435688

9th Global Edition

Authors: Richard Johnson, Irwin Miller, John Freund

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Question Posted: Apr 23, 2024 07:00 AM

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Let (X) and (Y) be independent normal random variables with [begin{array}{lll}E(X)=4 & text { and } &

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Probability And Statistics For Engineers

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