Unbiased Estimate of Population Mean, 
$\mu =\overline{x}=\frac{\sum{x}}{n}=\frac{\sum{\left( x-a \right)}}{n}+a$ where $a$ is a constant.
Unbiased Estimate of Population variance, 
${{s}^{2}}=\frac{1}{n-1}{{\sum{\left( x-\overline{x} \right)}}^{2}}=\frac{1}{n-1}\left[ \sum{{{x}^{2}}}-\frac{{{\left( \sum{x} \right)}^{2}}}{n} \right]$ 	[in MF 26]
$=\frac{n}{n-1}\times $(sample variance) or $\frac{n}{n-1}{{\sigma }_{x}}^{2}$where ${{\sigma }_{x}}^{2}$ is the sample variance.
$=\frac{1}{n-1}\left[ \sum{{{(x-a)}^{2}}}-\frac{{{\left( \sum{(x-a)} \right)}^{2}}}{n} \right]$ where $a$ is a constant.

$\mu =\overline{x}=\frac{\sum{x}}{n}=\frac{\sum{\left( x-a \right)}}{n}+a$ where $a$ is a constant.

Unbiased Estimate of Population variance, 

${{s}^{2}}=\frac{1}{n-1}{{\sum{\left( x-\overline{x} \right)}}^{2}}=\frac{1}{n-1}\left[ \sum{{{x}^{2}}}-\frac{{{\left( \sum{x} \right)}^{2}}}{n} \right]$ 	[in MF 26]

$=\frac{n}{n-1}\times $(sample variance) or $\frac{n}{n-1}{{\sigma }_{x}}^{2}$where ${{\sigma }_{x}}^{2}$ is the sample variance.

$=\frac{1}{n-1}\left[ \sum{{{(x-a)}^{2}}}-\frac{{{\left( \sum{(x-a)} \right)}^{2}}}{n} \right]$ where $a$ is a constant. 

Unbiased estimate of Population Parameters

Unbiased estimate of Population Parameters

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