If each observation of a raw data whose variance is {sigma ^2} , is multiplied by λ , then variance

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13.Statistics

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If each observation of a raw data whose variance is ${\sigma ^2}$, is multiplied by $\lambda$, then the variance of the new set is

A

${\sigma ^2}$

B

${\lambda ^2}{\sigma ^2}$

C

$\lambda + {\sigma ^2}$

D

${\lambda ^2} + {\sigma ^2}$

Solution

We know $Var ( ax + b )= a ^2 \cdot V$ ar $( x )$

Here $a = \lambda , b =0$

$\therefore Var ( \lambda x )= h ^2 \cdot Var ( x )= \lambda ^2 \sigma^2$

Standard 11

Mathematics

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