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13.Statistics
normal
પ્રથમ $n$ પ્રાકૃતિક સંખ્યાઓનું વિચરણ શોધો.
A
$n^2 + 1$
B
$\frac{{{n^2}\, + \,\,1}}{6}$
C
$\frac{{{n^2}\, - \,\,1}}{{12}}$
D
આપેલ પૈકી એકપણ નહિં.
Solution
$\,{\sigma ^2}\,\, = \,\,\frac{{\Sigma x_i^2}}{n}\,\,\, – \,\,{\left( {\frac{{\Sigma {x_i}}}{n}} \right)^2}\,\,\,\, = \,\,\frac{{\Sigma {n^2}}}{n}\,\, – \,\,{\left( {\frac{{\Sigma n}}{n}} \right)^2}\,\,$
$ = \,\,\frac{{n(n\,\, + \,\,1)\,(2n\,\, + \,\,1)}}{{6n}}\,\, – \,\,\left\{ {\frac{{n{{(n\, + \,\,1)}^2}}}{{2n}}} \right\}\,\,\,\,\, = \,\,\frac{{{n^2}\, – \,\,1}}{{12}}$
Standard 11
Mathematics
