Question about the variance of normal distribution

[A X]

 

I am confused with the equation a+4+b=0 and the following variance equation. In my opinion, in order to let the combined mean to be zero, it should be:

a * (mean of X1) + 4 * (mean of X2) + b * (mean of X3) = 0

 

and for the variance part, it should be:

(a^2) * (variance of X1) + (4^2) * (variance of X2) + (b^2) * (variance of X3) = 1

 

Appreciate for the help.

[Author]

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