Let & be a persistent recurrent event and N, the number of occurrences of in trials. Prove that (12.3) E(N) = u + + +2 and hence that E(N) is the coefficient of s* in (12.4) F2 (s) + F(s) (1-s){1-F(s)}2 (Note that this may be reformulated more elegantly using bivariate generating functions.)