if $i \neq j$ what is $Cov[X_i, X_j]$ ?

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- Apr 14th 2014, 09:21 AM #1

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## Covarance question

Let X1 , . . . be independent with common mean μ and common variance σ 2 , and set . For , find .

If then

If then I don't see how I can do anything with this statement.

or I want to just apply the definition of covariance, , to get , which seems too complicated to be helpful.

- Apr 14th 2014, 09:43 AM #2

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- Apr 14th 2014, 10:51 AM #3

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## Re: Covarance question

Ya that's muh question :P.

Do you mean to say that I should use this theorem I have laying around $ Cov(\sum_{i=1}^{n}X_i , \sum_{j=1}^{m}X_j) = \sum_{i=1}^{n}\sum_{j=1}^{m} Cov(X_i, X_j)$?

If then the remaining two pairs of $X's$ would sum up to $2\sigma^2$?

Since $Cov(X_n , 0)=Cov(X_n , 0*X_n)=0*Cov(X_n , X_n)$?

- Apr 14th 2014, 11:07 AM #4

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- Apr 14th 2014, 03:06 PM #5

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