14. Wald’s equation can be used as the basis of a proof of the elementary renewal theorem. Let X1,X2,... denote the interarrival times of a renewal process and let N(t) be the number of renewals by time t.

(a) Show that whereas N(t) is not a stopping time, N(t) + 1 is.

Hint: Note that N(t) = n ⇔ X1 +···+ Xn  t and X1 +···+ Xn+1 > t

(b) Argue that?