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Math Help - Sample Mean Definition

  1. #1
    Senior Member BAdhi's Avatar
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    Sample Mean Definition

    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...
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  2. #2
    Grand Panjandrum
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    Re: Sample Mean Definition

    Quote Originally Posted by BAdhi View Post
    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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