1. ## Sample Mean Definition

This is regarding the concept of sample mean

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

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

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

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 $\displaystyle X$.But if it is true how can $\displaystyle E(x_i)=\mu$ ? because $\displaystyle x_i$ is a constant.

Any help is greatly appreciated...

2. ## Re: Sample Mean Definition

This is regarding the concept of sample mean

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

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

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

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 $\displaystyle X$.But if it is true how can $\displaystyle E(x_i)=\mu$ ? because $\displaystyle x_i$ is a constant.

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

CB