A) \[\frac{a}{c}\sigma \]
B) \[\left| \frac{a}{c} \right|\sigma \]
C) \[\left| \frac{c}{a} \right|\sigma \]
D) \[\frac{c}{a}\sigma \]
Correct Answer: B
Solution :
Let\[Y=\frac{aX+b}{c}\] Then\[\overline{Y}=\frac{1}{c}(a\overline{X}+b)\Rightarrow Y-\overline{Y}=\frac{a}{c}(X-\overline{Y})\] \[\Rightarrow \]\[\frac{1}{N}\sum {{(Y-\overline{Y})}^{2}}=\frac{{{a}^{2}}}{{{c}^{2}}}\frac{1}{N}\sum {{(X-\overline{X})}^{2}}\] There fore S.D. of Y \[=\sqrt{\frac{{{a}^{2}}}{{{c}^{2}}}\frac{1}{N}\sum {{(X-\overline{X})}^{2}}}=\sqrt{\frac{{{a}^{2}}}{{{c}^{2}}}\sigma }=\left| \frac{a}{c} \right|\sigma \]
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