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    Consider the sequence Yi, i = 1, 2,...
    which consists of independent and identically distributed random variables with Yi~N(u; 1) for some uER. We define the
    n-th sample average as

    Xn = (1/n)Sum from 1 to n of Yi

    I need to show that Xn tends to u i.e the mean.

    Any help would be much appreciated.
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    Disclaimer: prob theory isn't my strong point. However...

    If X and Y are independent normal variables with common mean u and s.d. s_x and s_y, what's the distribution of X + Y?

    You can use this and induction to deduce the distribution of Y1+Y2+...+Y_n.

    From there it should be easy.
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    (Original post by DFranklin)
    Disclaimer: prob theory isn't my strong point. However...

    If X and Y are independent normal variables with common mean u and s.d. s_x and s_y, what's the distribution of X + Y?

    You can use this and induction to deduce the distribution of Y1+Y2+...+Y_n.

    From there it should be easy.
    Ok i'll give it a go, thankd.
 
 
 
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