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?