I want to establish some of the properties of Poisson processes that were employed in Chapters 3 and 6 and were either left unproven there or explained by simple heuristics. Certain standard results, such as the mean and variance of a Poisson distribution, can be found in the books by Ross [99, 100], the ones chosen among the many other possible references in probability that could have been cited.
Note that throughout this appendix I assume a certain familiarity with the notion of conditioning one random variable on another, as explained, for example, in Chapters 6 and 7 of Ross  and in Appendix D.
To begin with, let’s return to two results stated but not proved in Section 3.2. First, Let Ni(t) be independent Poisson ...