$\displaystyle

S^2 = \frac{x-u}{n - 1} and S^2= \frac{x-u}{n }

$

I cant type the summation sign and x bar so i use u

Show that one is biased and unbiased

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- Dec 16th 2009, 07:50 AMwantanswersbiased and unbiased
$\displaystyle

S^2 = \frac{x-u}{n - 1} and S^2= \frac{x-u}{n }

$

I cant type the summation sign and x bar so i use u

Show that one is biased and unbiased - Dec 16th 2009, 05:14 PMmatheagle
what is u?

the sample mean is \bar X

the sum is \sum{i=1}^n X_i

are the X's from any particular distribution? - Dec 17th 2009, 08:57 AMnovice
You mean is this:

$\displaystyle s^2=\frac{(X-\overline X)^2}{N}$ and $\displaystyle s^2=\frac{(X-\overline X)^2}{N-1}$

$\displaystyle \sigma^2= s^2=\frac{(X-\overline X)^2}{N}$ is the of the population variance and is unbiase, assuming that the population is infinite. It is like drawing balls from an urn with replacement, and it is also true according to the Central Limit Theorem.

On the other hand, the variance of the sample is not infinit, it is bias and just like drawing balls from an urn without replacement. Therefore, for a better estimate of the variance from a given sample, a correction factor $\displaystyle \frac{N}{N-1}$ is used.

The corrected estimate of sample variance becomes $\displaystyle (\frac{N}{N-1})\sigma^2= (\frac{N}{N-1})(\frac{(X-\overline X)^2}{N})$, and the result is $\displaystyle s^2=\frac{(X-\overline X)^2}{N-1}$ - Dec 18th 2009, 04:49 PMmatheagle
Is there a summation here? what is this U?.......

And I'm dying at ask 'what's a matta u'?

The Adventures of Rocky and Bullwinkle - Wikipedia, the free encyclopedia

The name of Bullwinkle's alma mater is Whassamatta U.

THis university was actually featured in the original cartoons,

though its exact location was never given; the film places it in Illinois.

Probably at my school? - Dec 19th 2009, 09:20 AMnovice
- Dec 20th 2009, 07:57 AMtheodds
That guy is biased for infinite populations. It is asymptotically unbiased though.

OP: You've left out at least some information, so I'll assume that $\displaystyle X_1, X_2, ... , X_n$ are iid, and that the terms are defined as Novice said above. Just take expectations, noting that $\displaystyle \sum _{i = 0} ^ n \left( X_i - \bar{X} \right) ^2 = \sum _{i = 0} ^ n X_i ^2 - n\bar{X}^2$. You'll have to flip around the formula $\displaystyle \mbox{Var} X = EX^2 - (EX)^2$, but it isn't more than a few lines.