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If SD of X is S, then SD of the variable M \( \Large \frac{aX+b}{c} \), where a, b, c are constants, is

A) \( \Large \|\frac{c}{a}\|\sigma \)
B) \( \Large \|\frac{a}{c}\|\sigma \)
C) \( \Large \|\frac{b}{c}\|\sigma \)
D) \( \Large \frac{c^{2}}{a^{2}}\sigma \)

Correct Answer:


B) \( \Large \|\frac{a}{c}\|\sigma \)

Description for Correct answer:
We know that

Therefore, \( \Large var \left(\frac{aX+b}{c}\right)= \left(\frac{a}{c}\right)^{2}\ var \left(X\right)=\frac{a^{2}}{c^{2}}\sigma^{2} \)

Therefore, \( \Large SD = \sqrt{var \left(\frac{aX+b}{c}\right) } = |\frac{a}{b}|\sigma \)

Part of solved Statistics questions and answers : >> Elementary Mathematics >> Statistics

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