Pure Mathematics
Statistics

Worked Example 3

Given that [latex]E\left( X \right)=3[/latex], [latex]\text{Var}\left( X \right)=4[/latex], [latex]\text{E}\left( Y \right)=-2[/latex]and [latex]\text{Var}\left( Y \right)=7[/latex] . Find the expectation and variance of

(i)

[latex]3X+2Y[/latex]

(ii)

[latex]2X-3Y[/latex]

(iii)

[latex]{{X}_{1}}+{{X}_{2}}-{{Y}_{1}}-{{Y}_{2}}-{{Y}_{3}}[/latex]

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