A) \[\left( \frac{a}{c} \right)\sigma \]
B) \[\left| \frac{a}{c} \right|\sigma \]
C) \[\left( \frac{{{a}^{2}}}{{{c}^{2}}} \right)\sigma \]
D) None of these
Correct Answer: B
Solution :
Let \[y=\frac{ax+b}{c}\Rightarrow y=\frac{a}{c}x+\frac{b}{c}\] \[\Rightarrow \] \[y=Ax+B,\] where \[A=\frac{a}{c}\] and \[B=\frac{b}{c}\] So, \[\overline{y}=A\overline{x}+B\] and hence \[y-\overline{y}=Ax+B-(A\overline{x}+B)=A(x-\overline{x})\] \[\Rightarrow \] \[{{(y-\overline{y})}^{2}}={{A}^{2}}{{)}^{2}}\] \[\Rightarrow \] \[\sum\limits_{{}}^{{}}{{{(y-\overline{y})}^{2}}}={{A}^{2}}\sum\limits_{{}}^{{}}{{{(x-\overline{x})}^{2}}}\] \[\Rightarrow \] \[n\sigma _{y}^{2}={{A}^{2}}(n\sigma _{x}^{2})\Rightarrow {{\sigma }_{y}}=|A|{{\sigma }_{x}}\]
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