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As mentioned, i have to calculate $\mathrm{Var}(6x+2)$ knowing that $E(X^2) = 6$ and $EX = 2$

I know that $$\mathrm{Var}(6X+2) = 6^2\mathrm{Var}(X) = 36 \mathrm{Var}(X) = 36 \cdot ( E[X^2] - E^2[X] ),$$ but i kinda stopped at this point because i don't know how to unfold this.

Is it just

$$36 \cdot ( 6 - (EX)^2 ) = 36 \cdot (6 - 4) = 72?$$

5xum
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learningbtw
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    @learningbtw: your calculations are correct. The result is 72 – tommik Oct 26 '21 at 15:42
  • @learningbtw, your solution is correct, yes. As long as you already know that $\mathrm{Var}(aX+b)=a^2\mathrm{Var}(X)$, your derivation is all you need. – 5xum Oct 26 '21 at 15:43

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