I have got G(s) = p+ $\ rs^2$ a p.g.f for a family size.
Let K be the total number of tumour cells produced from a single original tumour cell
Let R(s) = P[K=0] + sP[K=1]+.... be the p.g.f of this number
Let the number of immediate descendants of the original cell be Z then K= 1+ $\ K_1+...+K_Z $ where$\ K_1...K_Z$ are independent random total numbers of cells produced by each of the immediate descendants
then R(s) = sG(R(s))
I can't figure the last statement out and therefore I can't follow the rest of the example which follows, can anyone explain this? thanks