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\[\overline{Y}=\frac{1}{c}(aX+b)\Rightarrow Y-\overline{Y}=\frac{a}{c}(X-\overline{X})\] \[\Rightarrow \]\[\frac{1}{N}\Sigma {{(Y-\overline{Y})}^{2}}=\frac{{{a}^{2}}}{{{c}^{2}}}\frac{1}{N}\Sigma {{(X-\overline{X})}^{2}}\] Therefore \[S.D.\] of \[Y\] \[=\sqrt{\frac{{{a}^{2}}}{{{c}^{2}}}\frac{1}{N}\Sigma {{(X-\overline{X})}^{2}}}=\sqrt{\frac{{{a}^{2}}}{{{c}^{2}}}{{\sigma }^{2}}}=\left| \frac{a}{c} \right|\sigma \]
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