Hi there,

Assume that and are independently and identically distributed random variables.

how do I show that and are independent.

Thanks

Casper

Printable View

- December 3rd 2008, 08:41 AMcasperycindependently and identically distributed random variables
Hi there,

Assume that and are independently and identically distributed random variables.

how do I show that and are independent.

Thanks

Casper - December 3rd 2008, 09:13 AMcl85
Check if they are uncorrelated. Uncorrelated normal random variables are independent of each other.

- December 3rd 2008, 10:07 AMcasperyc
- December 3rd 2008, 10:21 AMcl85
and are both linear combination of independent normal random variables and are hence normal. To check if two normal random variables are independent, we just need to check if they are uncorrelated, ie, their covariance equal 0.

- December 3rd 2008, 11:28 AMcasperyc
- December 3rd 2008, 01:04 PMcasperyc
let

when I calculate the

I cant find the

how should I proceed? I dont think it's a good way to proceed....

anyone else got an idea?

Thanks

Casper - December 3rd 2008, 02:13 PMcl85
- December 3rd 2008, 02:23 PMcasperyc
- December 3rd 2008, 02:41 PMcl85
No! My example is not to give you a formula to use, it's to show you how to rearrange terms when doing covariance.