I was given the problem above. I am confused on how to find the variance of the linear combinations.
A for example would have a mean of 22 correct? Can someone explain how I can use that info to find the variance for A?
2026-05-05 20:59:42.1778014782
Variance of a linear combinations
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You are correct that $E[2X+20]=2E[X]+20=22$.
For the variance, you want $$E[(2X+20)^2]-(E[2X+20])^2 = E[4X^2+40X+400]-22^2$$ $$=4E[X^2]+40E[X]+400-22^2 $$ and you know $E[X^2]$ and $E[X]$.
All the others are similar, though you should note that as $X$ and $Y$ are assumed to be independent you have $E[XY]=E[X]E[Y]$.