It would have been better if you had shown how you got to this result...

But if I understand correctly what you just did, it's not the correct way. You have to start from , where is the number of offspring for the individual i, and the are iid with mean and variance

To do this, use the law of total variance, by conditioning to :

But it is commonly known that for a GW process (shown by induction).

Thus , I can't find the mistake, so if you do....

Hmm so I find