Mean + Variance

July 14th, 2010

The mean and variance are some of the most used in math and statistics. Below are some Math Formulas of the mean and variance.

$Mean + Variance estimator$ is an unbiased estimator. You can prove this by using: $Mean and variance$

If $Mean and variance$ for all n > 1, then the Central Limit Theorem says that: $Proof mean and variance$ (a Normal distribution).

Confidence Interval for µ

$Confidence interval of mean$

You can prove this by using:

$Confidence interval proof$

If the sample is small, to retain 95% CI, you have to widen the interval. To do that, you replace Z _0.025 by t _0.025. Then either:

$Estimating mean$ and Z 0.025 = 1.96

OR

$Estimate mean$

If you don’t know $zigma$ for certain, you can use t _0.025 instead of Z to compensate for S.

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