IfSDof X is S,thenSDofthevariable μ=aX+bc, where a,b and c areconstants,is

A
$|\frac{c}{a}| σ$
B
$|\frac{a}{c}| σ$
C
$|\frac{b}{c}| σ$
D
$\frac{c^{2}}{a^{2}} σ$

Solution:

We know that,

$\begin{array}{l} var (aX + b) = a^{2} var (X) \\ ∴ var (\frac{aX + b}{c}) = {(\frac{a}{c})}^{2} var (X) = \frac{a^{2}}{c^{2}} σ^{2} \\ ∴ SD = \sqrt{var (\frac{aX + b}{c})} = |\frac{a}{c}| σ \end{array}$

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