Hi,
I have the following problem:
There is a random Gaussian variable with and is a standard nomally distributed variable with mean 0 and variance 1.
Under some filtration generated by , I have to find .
Therefore I calculated the mean (with use of martingale property):
Now I have to calculate the variance (Var):
To determine the covariance I proceed as follow:
because of the independency ?
Is that correct?