Linear Combinations of Normal Random Variables

Linear Combinations of Normal Random Variables

Given that \(X\)~\(N(3,4)\) and \(Y\)~\(N(-2,7)\). Find the normal distribution of

\(3X+2Y\)
\(2X-3Y\)
\(X_{1}+X_{2}-Y_{1}-Y_{2}-Y_{3}\)

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Answer:(i) \(N(5,64)\) (ii) \(N(12,79)\) (iii) \(N(12,29)\)

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