The Student Room Group

Variance of the Sample Mean (Normal Population)

Screen Shot 2016-05-04 at 12.35.06.pngPlease see screenshot - Could someone please explain to the me steps.

In particular, why when taken outside of the sum does 1/n become 1/n2
Then after that why does the o2 come into play?
Help appreciated.
Original post by JKITFC
Screen Shot 2016-05-04 at 12.35.06.pngPlease see screenshot - Could someone please explain to the me steps.

In particular, why when taken outside of the sum does 1/n become 1/n2
Then after that why does the o2 come into play?
Help appreciated.


If X is a random variable and a is a scalar, then var(aX)=a2var(x)var(aX) = a^2 var(x). Just look at the formula for variance. The σ2\sigma^2 comes from the fact that the XiX_i are identically distributed each with variance σ2\sigma^2

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