Statistics of Satellites That Are Launched at Regular Intervals and Have an Exponential Distribution of Lifetimes

摘要

This note describes a method for computing the answers to the following questions concerning the satellites described in the title: (a) What is the probability of having m live satellites in orbit immediately after the nth launch. (b) What is the probability of having m live satellites in orbit for the first time immediately after the nth launch. Question (b) arises, for example, when the task of putting up an initial set of m communication satellites is considered.