InterviewSolution
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InterviewSolution
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Given that `barx` is the mean and `sigma^(2)` is the variance of `n` observations `x_(1),x_(2),………….x_(n)`. Prove that the mean and variance of the observations `ax_(1),ax_(2),ax_(3),………….ax_(n)` are `abarx` and `a^(2)sigma^(2)` , respectively, `(a!=0)` |
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Answer» Mean of `n` observations `barx=(x_(1)+x_(2)+…………..+x_(n))/n=(sumx_(i))/nimpliessumx_(i)=n.barx`………….1 Variance `sigma^(2)=(sum(x_(i)-barx)^(2))/n` `implies sum(x_(i)-barx)^(2)= nsigma^(2)`…………….2 Now mean of observation `ax_(1),ax_(2),………..,ax_(n)` `barx=(ax_(1)+ax_(2)+..............+ax_(n))/n=(a(x_(1)+x_(2)+..........+x_(n)))/n` `=(asumx_(i))/n=(a.nbarx)/n=abarx`............3 Hence Proved. and variance `=((sumX_(i)-barX)^(2))/n=1/nsum(ax_(i)-abarx)^(2)` `=a^(2)sigma^(2)` Hence Proved. |
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