Let be a column vector of independent N(0,1) distributed random variables. Let A be an orthogonal matrix.

Prove that using moment generating functions.

Printable View

- August 29th 2009, 06:54 AMRoyalFlushVector of independent normal RV's - mgfs
Let be a column vector of independent N(0,1) distributed random variables. Let A be an orthogonal matrix.

Prove that using moment generating functions. - August 29th 2009, 09:00 AMmatheagle
And where does this A come in?

Do you want AX?

via moment generating functions.

Each and the sum is - August 29th 2009, 10:48 PMRoyalFlush
- August 29th 2009, 11:01 PMmatheagle
Let and

If they are independent, then the MGF of the sum is the product of the individual MGFs.

So

Thus

NOW, let which shows that

the sum of any two independent s

is a , you just add the degrees of freedom.

This can easily be extended to n random variables.