Let be i.i.d. sampes from Let

Prove that and are uncorrelated for any

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- Mar 5th 2010, 01:49 PMAnonymous1Correlation of samples
Let be i.i.d. sampes from Let

Prove that and are uncorrelated for any - Mar 5th 2010, 10:13 PMmatheagle
for simplicity let i=1....

Let's obtain the covariance between and

Now find the covariance between each pair, taking one term from each set.

ALL we need is for the for each , we don't need NORMALITY...

Next use the fact that all the variances are equal this becomes zero.

Changing 1 to i is easy, just sum over all the terms that's not i in the second sum.