ધારો કે x_1, x_2 ……, x_n એ વિચ | vedclass

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Question

આપણી પાસે $\,{	ext{Var(Y)}}\,\,$

$ = \,\,\frac{{	ext{1}}}{{	ext{n}}}\,\,\sum\limits_{i\, = \,1}^n {{{({y_i}\, - \,\,\bar y)}^2}} \,\,\,\,\,

Vedclass · Accepted Answer

$V(Y) = a^2V(X)$

Vedclass · Answer

આપણી પાસે $\,{	ext{Var(Y)}}\,\,$

$ = \,\,\frac{{	ext{1}}}{{	ext{n}}}\,\,\sum\limits_{i\, = \,1}^n {{{({y_i}\, - \,\,\bar y)}^2}} \,\,\,\,\,\,[\because \,\,{y_i}\,\, = \,\,a{x_i}\, + \,\,b\,;\,\,i\,\, = \,\,1,\,2,\,......,\,\,n\,\, \Rightarrow \,\,\bar Y\,\, = \,\,a\,\bar X\,\, + \,\,b]$

$ \Rightarrow \,\,{	ext{Var(Y)}}\,\, = \,\,\frac{{	ext{1}}}{{	ext{n}}}\,\,\sum\limits_{i\, = \,1}^n {{a^2}{{({x_i}\, - \,\,\bar X)}^2}} \,\,\,\,\,\,\,\,\,$

$ \Rightarrow \,\,Var(Y)\,\, = \,\,{a^2}\left\{ {\frac{1}{n}\,\sum\limits_{i\, = \,1}^n {{{({x_i}\, - \,\,\bar X)}^2}} } ight\}\,\, = \,\,{a^2}Var(X)$

$X$	$1$	$3$	$5$	$7$	$9$
આવૃતિ $(f)$	$4$	$24$	$28$	$\alpha$	$8$

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