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# Converge in probability Watch

1. 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.
2. 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.
3. (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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Updated: December 8, 2010
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