# Central Limit Theorem

• Feb 1st 2008, 05:55 PM
syaaram7805
Central Limit Theorem
Can someone please give me a hint as to what I am supposed to be looking for here? I have searched my textbook front to back and the internet and am so confused. Please help! Thanks!

State the main points of the Central Limit Theorem for a mean.
• Feb 1st 2008, 07:20 PM
mr fantastic
Quote:

Originally Posted by syaaram7805
Can someone please give me a hint as to what I am supposed to be looking for here? I have searched my textbook front to back and the internet and am so confused. Please help! Thanks!

State the main points of the Central Limit Theorem for a mean.

One conclusion of the Central Limit Theorem is that if $\displaystyle Y_1$, $\displaystyle Y_2$, ..... $\displaystyle Y_n$ are independent and identically distributed random variables with $\displaystyle E(Y_i) = \mu$ and $\displaystyle Var(Y_i) = \sigma^2$ both finite, then $\displaystyle \bar{Y} = \frac{1}{n} \sum_{i=1}^n Y_i$ is asymptotically normal with mean $\displaystyle \mu$ (and variance $\displaystyle \frac{\sigma^2}{n}$).
• Feb 2nd 2008, 09:07 AM
syaaram7805
Central Limit Theorem
Thank you so much for helping understand what this was looking for. Now that I have read that I think I know where to go from here. Thanks so much!
• Feb 2nd 2008, 11:34 AM
CaptainBlack
Quote:

Originally Posted by mr fantastic
One conclusion of the Central Limit Theorem is that if $\displaystyle Y_1$, $\displaystyle Y_2$, ..... $\displaystyle Y_n$ are independent and identically distributed random variables with $\displaystyle E(Y_i) = \mu$ and $\displaystyle Var(Y_i) = \sigma^2$ both finite, then $\displaystyle \bar{Y} = \frac{1}{n} \sum_{i=1}^n Y_i$ is asymptotically normal with mean $\displaystyle \mu$ (and variance $\displaystyle \frac{\sigma^2}{n}$).

Quote:

Originally Posted by syaaram7805
Can someone please give me a hint as to what I am supposed to be looking for here? I have searched my textbook front to back and the internet and am so confused. Please help! Thanks!

State the main points of the Central Limit Theorem for a mean.

What Mr F writes is the gist of the very first hit by Google for the search string "central limit theorem for mean".

RonL