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

Results 1 to 5 of 5

- Apr 14th 2014, 10:21 AM #1

- Joined
- Oct 2009
- From
- Detroit
- Posts
- 220
- Thanks
- 5

## 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, 10:43 AM #2

- Joined
- Nov 2013
- From
- California
- Posts
- 4,900
- Thanks
- 2041

- Apr 14th 2014, 11:51 AM #3

- Joined
- Oct 2009
- From
- Detroit
- Posts
- 220
- Thanks
- 5

## 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, 12:07 PM #4

- Joined
- Nov 2013
- From
- California
- Posts
- 4,900
- Thanks
- 2041

- Apr 14th 2014, 04:06 PM #5

- Joined
- Oct 2009
- From
- Detroit
- Posts
- 220
- Thanks
- 5