Given that $E\left( X \right)=3$, $\mathrm{Var}\left( X \right)=4$, $\mathrm{E}\left( Y \right)=-2$a

Question

Given that $E\left( X \right)=3$, $\mathrm{Var}\left( X \right)=4$, $\mathrm{E}\left( Y \right)=-2$and $\mathrm{Var}\left( Y \right)=7$ . Find the expectation and variance of $3X+2Y$ $2X-3Y$ ${{X}_{1}}+{{X}_{2}}-{{Y}_{1}}-{{Y}_{2}}-{{Y}_{3}}$

Accepted Answer

(i) $E = 5$, $\text{Var} = 64$; (ii) $E = 12$, $\text{Var} = 79$; (iii) $E = 12$, $\text{Var} = 29$

Worked Example 3

Worked Example 3

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