It looks as though π is meant to be the limit of the increasing sequence given by . Needless to say, π here does not mean the number 3.14159... .
I don't know what the connection with expectations is. That must come from some previous information.
Is anyone familiar with this theorem:
If E(X) > 1 then the extinction probability is the unique root of the equation , which lies strictly between 0 and 1.
If E(X) < 1, then
Graph is below:
I cannot seem to find any link between the expectations, and the curve f(x) and y=x in the graph. And what is the meaning of ?
Thanks for your attention.