Q. If SD of $X$ is $s$, then SD of the variable $\mu = \frac{aX + b}{c}$, where $a,\ b,\ c$ are constants, is
A) $\left| \frac{c}{a} \right|\sigma$
B) $\left| \frac{a}{c} \right|\sigma$
C) $\left| \frac{b}{c} \right|\sigma$
D) $\left| \frac{c^{2}}{a^{2}} \right|\sigma$
Explanation
(b)
We know that,
$var(aX + b) = a^{2}var(X)$
$\therefore\ var\left( \frac{aX + b}{c} \right) = \left( \frac{a}{c} \right)^{2}var(X) = \frac{a^{2}}{c^{2}}\sigma^{2}$
$\therefore\ SD = \sqrt{var\left( \frac{aX + b}{c} \right)} = \left| \frac{a}{c} \right|\sigma$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.