Question

If $X$ is a random variable such that $\sigma \left(X\right)=2.6$, then $\sigma (1-4X)$ is equal to,

• A. $7.8$
• B. $-10.4$
• C. $13$
• D. $10.4$

Answer 1

The correct option is D $10.4$

Standard deviation $\sigma$ satisfies the following relation:
$\sigma (aX+b)=\left|a\right|\left(\sigma \right(X\left)\right)$

$\therefore \sigma (1-4X)=|-4|\sigma \left(X\right)=4\times 2.6=10.4$