mean and variance of population distribution - law of large numbers - plz help

**homalina** · September 21st 2012, 07:32 AM

A population distribution has a mean of 10 and a variance of 16. Determine the mean and variance of Ybar from an i.i.d. sample from this population for a) n=10, b) n= 100 and c) n=1000. Relate the answers to the law of large numbers.

Please advise how to start this question?

**harish21** · September 21st 2012, 08:31 AM

Originally Posted by homalina

A population distribution has a mean of 10 and a variance of 16. Determine the mean and variance of Ybar from an i.i.d. sample from this population for a) n=10, b) n= 100 and c) n=1000. Relate the answers to the law of large numbers.

Please advise how to start this question?

For iid $Y_1,\cdots, Y_n$ with mean and variance $\mu\;&\;\sigma^2$
$\bar{Y}=\dfrac{1}{n}\sum_{i=1}^n Y_i=\mu$

$E[\bar{Y}]=\dfrac{1}{n}\sum_{i=1}^n E[Y_i]=\mu$

also, $Var(\bar{Y})=\dfrac{1}{n^2}\sum_i {\sigma_i}^2=...$

**homalina** · September 22nd 2012, 09:03 AM

Thanks a lot

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