Sample Mean Definition

**BAdhi** · September 27th 2011, 02:09 AM

This is regarding the concept of sample mean

I know that $\bar{x}$ is defined as follows

$\bar{x}=\frac{x_1+x_2+x_3+x_4+\dots+x_n}{4}$

what I want to know is that what really is $x_i$

according to the notes and other references that i've referred, currently i believe that it is sample of values that is taken from the random variable $X$ .But if it is true how can $E(x_i)=\mu$ ? because $x_i$ is a constant.

Any help is greatly appreciated...

**CaptainBlack** · September 27th 2011, 02:40 AM

Originally Posted by BAdhi

This is regarding the concept of sample mean

I know that $\bar{x}$ is defined as follows

$\bar{x}=\frac{x_1+x_2+x_3+x_4+\dots+x_n}{ n}$

what I want to know is that what really is $x_i$

according to the notes and other references that i've referred, currently i believe that it is sample of values that is taken from the random variable $X$ .But if it is true how can $E(x_i)=\mu$ ? because $x_i$ is a constant.

Any help is greatly appreciated...

Consider $X_1,..X_n$ iidd RV with $X_i, \ \ i=1..n$ distributed as $X$ , then $x_i$ is an instance of the i-th element of a sample but $X_i$ is a random variable with $E(X_i)=E(X)$

CB

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