Gujarati
13.Statistics
easy

किसी चर $x$ का मानक विचलन है। तब चर $\frac{{ax + b}}{c}$ का मानक विचलन है, (जहाँ $a, b, c$ अचर है)

A

$\left( {\frac{a}{c}} \right)\,\sigma $

B

$\left| {\frac{a}{c}} \right|\,\sigma $

C

$\left( {\frac{{{a^2}}}{{{c^2}}}} \right)\,\sigma $

D

ईनमे से कोई नहीं

Solution

(b)माना $y = \frac{{ax + b}}{c}$

अर्थात् $y = \frac{a}{c}x + \frac{b}{c}$

अर्थात् $y = Ax + B$, जहाँ $A = \frac{a}{c}$,$B = \frac{b}{c}$

 $\bar y = A\bar x + B$

 $y – \bar y = A(x – \bar x)$ ==> ${(y – \bar y)^2} = {A^2}{(x – \bar x)^2}$

==> $\sum {(y – \bar y)^2} = {A^2}\sum {(x – \bar x)^2}$

==> $n.\sigma _y^2 = {A^2}.n\sigma _x^2$ ==> $\sigma _y^2 = {A^2}\sigma _x^2$

==> ${\sigma _y} = \,|A|{\sigma _x}$ ==> ${\sigma _y} = \,\left| {\frac{a}{c}} \right|{\sigma _x}$

अत: नया $S.D.$ $ = \left| {\frac{a}{c}} \right|\,\sigma $.

Standard 11
Mathematics

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