Suppose g(z) = p/(1 − qz), i.e. that the offspring distribution is geometric G0(p). Show that, when p = q, then Find the pgf of Yn ≡ Xn|Xn = 0. Find gn(z) when p = 1/2, and show that the chance of...

Suppose g(z) = p/(1 − qz), i.e. that the offspring distribution is geometric G0(p). Show that, when p = q, then

Find the pgf of Yn ≡ Xn|Xn = 0. Find gn(z) when p = 1/2, and show

that the chance of extinction in generation n is 1/(n(n+1)). Find the

distribution of Yn defined as before, and deduce that Yn/n D

→ E(1).