There is a theorem from renewal theory called Blackwell's Renewal Theorem (see Ross ([52], Prop. 3.5.1) that is applicable to processes with integer-valued renewal times that are otherwise non-periodic. It implies the following for delayed renewal processes: the expected number of renewals exactly at time \(n\) converges to the reciprocal of the mean inter-renewal time as \(n \longrightarrow \infty\). Prove parts (c) and (d) of Theorem 1 of Section 4.5 by presuming that the hypotheses of Blackwell's Theorem are in force, and considering the sequence of random variables \(I_{0}, I_{1}, I_{2}, \ldots\), defined by setting \(I_{n}\) to 1 or 0 according to whether \(X_{n}\) equals \(j\) or not.