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

• Sep 21st 2012, 07:32 AM
homalina
mean and variance of population distribution - law of large numbers - plz help
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.

• Sep 21st 2012, 08:31 AM
harish21
Re: mean and variance of population distribution - law of large numbers - plz help
Quote:

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.

For iid $\displaystyle Y_1,\cdots, Y_n$ with mean and variance $\displaystyle \mu\;&\;\sigma^2$
$\displaystyle \bar{Y}=\dfrac{1}{n}\sum_{i=1}^n Y_i=\mu$
$\displaystyle E[\bar{Y}]=\dfrac{1}{n}\sum_{i=1}^n E[Y_i]=\mu$
also, $\displaystyle Var(\bar{Y})=\dfrac{1}{n^2}\sum_i {\sigma_i}^2=...$