so that .
. Hence (assuming ).
Pray tell, how do you propose to work these out merely using the mean and variance of and ?
Given that ~ , ~ and ~ , I need to find and and hence deduce and using iterated expectation and variance formulae.
I know that
Surely, I should just be able to find and without going through and , shouldn't I? Since I know and .
How would I work out and , and is there a reason why I would need to work these out before coming to my answers for and ?