Question

If s.d,of X is $\sigma ,$then s.d.of the variable $U=\frac{aX+b}{c}$ 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. $\frac{c^2}{a^2}\sigma$

Answer 1

Answer: (B)

$\left|\frac{a}{c}\right|\sigma$

We know, $Var(aX+b)=a^2.Var\left(x\right)$

Therefore we have $Var\left\{\frac{aX+b}{c}\right\}=\frac{a^2}{c^2}var\left(X\right)=\frac{a^2}{c^2}{\sigma }^2$

$\Rightarrow S.D\left\{\frac{aX+b}{c}\right\}=\left|\frac{a}{c}\right|\sigma$