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I don't understand , here $X$ is data like for ex. height in a class :

$X_1=186cm$

$X_2=186.9cm$

$X_3=188cm$

and so on ... or they are independent random vars like one var for height other for weight and so on ?

The first step is confusing for me , please explain the following :

The variance of $T=(X_1+X_2+X_3 + ... X_n)$ is $n\sigma^2$

Why ?

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The variance of the sum of independent random variables is the sum of their variances. So if $X_1$, $X_2$... all have variance $\sigma^2$ then the sum is $n\sigma^2$.

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  • $\begingroup$ so the $X_i$ here are all random vars, it confused me because the article says observations .... so I thought that they meant observations for a particular random var. $\endgroup$ – Oleg Mar 22 '17 at 0:24
  • $\begingroup$ Each observation is a different random variable. Think about surveying people and measuring their height. Your first measurement is 5' 10". But you could have picked somebody different and got a different height. $\endgroup$ – dash2 Mar 22 '17 at 0:27
  • $\begingroup$ thanks, I coined the wrong term in my head about a random var. $\endgroup$ – Oleg Mar 22 '17 at 7:37

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