very short question variance iid

[leo nidas]

Let x1, x2,...xn iid random variables.

Suppose that it is given that Var(Sum(x(i)))=S,
can I claim that var(x(i))=S/n ?


I guess that the correct answer is yes but the above result would not hold if we did not know the "iid" part.

Please let me know if I am correct.

Thanx in advance for any answers!

[BGM]

It is correct I think.

[Dason]

As long as by x(i) you mean the ith variable in the iid sample and not the ith order statistic. If that's what you mean then you should be fine and the result you stated holds.