CT3 Normal distribution

Hii all. There's two qus. in which i need someone to clarify the difference.
Ch.6- pg 37 - Exam style qus
Q&A bank part 2- Qus.2.20
Both have X and Y normally distributed. But In q 2.20 the dist. of X-2Y is taken as
N(1800-2×1200,300^2+4×500^2) here for variance ,they have squared 2 . But in Exam style why they used 3 and 4 in varince instead of squaring it?
Thanks in advance for prompt rply.

 

There's a difference between \( X_1 + X_2 \) and \( 2X \)

E.g.
\( X_1 + X_2 \) is roll two dice and add their score. ( \( X_1 , X_2 \) are IIDs)
\( 2X \) is roll a single and double the score.

The mean is same in both the cases but variance is higher in \( 2X \)

\(Var ( X_1 + X_2 ) = Var(X_1) + Var(X_2) = 2 \ Var(X) \) [ Exam style ques ]
\(Var ( 2X ) = 4 \ Var(X) \) [ Ques 2.20 ]

 

ohh okk. Thankyou