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