यदि प्रेक्षणों {x_1},,{x_2},,......{x_n} का प | vedclass

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Question

Varivence of $x_1 \cdot x_2 \cdot \cdots \quad x_n=6^2$

Variane of $a x_1 a x_2, \ldots a x_n=$ ?

varience $=\sigma^2=\frac{1}{n} \sum \limits_{

Vedclass · Accepted Answer

${a^2}{\sigma ^2}$

Vedclass · Answer

Varivence of $x_1 \cdot x_2 \cdot \cdots \quad x_n=6^2$

Variane of $a x_1 a x_2, \ldots a x_n=$ ?

varience $=\sigma^2=\frac{1}{n} \sum \limits_{i=1}^r y_i\left(n_i-\bar{x}ight)^2$

If each obs is weltiplied $2 y$ a the $y_i=a x_i \quad i . e \quad x_i=\frac{1}{a} y_i$

$y_i=a x_i n$

$	herefore \bar{y}=\frac{1}{n} \sum\limits_{i=1}^n y_i=\frac{1}{n} \sum\limits_{i=1}^n a x_i=\frac{a}{n} \sum\limits_{i=1}^n x_i=a \bar{x} .$

${\left[\because \bar{x}=\frac{1}{n} \sum\limits_{i=1}^n x_iight]}$

$(1) \Rightarrow \quad \sigma^2=\frac{1}{A} \sum_{i=1}^n\left(\frac{1}{a} y_i-\frac{1}{a} \bar{y}ight)^2$

$\Rightarrow a a^2 \sigma^2=\frac{1}{n} \sum_{i=1}^n\left(y_i-\bar{y}ight)^2$

These varieme of new obs' is $a^2 \sigma^2$

अंक	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
समूह $A$	$9$	$17$	$32$	$33$	$40$	$10$	$9$
समूह $B$	$10$	$20$	$30$	$25$	$43$	$15$	$7$

यदि प्रेक्षणों ${x_1},\,{x_2},\,......{x_n}$ का प्रसरण ${\sigma ^2}$ है, तब $a{x_1},\,a{x_2},.......,\,{\rm{ }}a{x_n}$, $a \ne 0$ का प्रसरण है

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