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» Solution :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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