Section 8.1 Introduction
In this chapter, you will investigate the relationship between number of successes over some interval. For each, one of these quantities will be fixed and the other one variable. First, consider the following:
Definition 8.1.1 Poisson Process
A Poisson process is a course of action in which:
- Successes in non-overlapping subintervals are independent of each other.
- The probability of exactly one success in a sufficiently small interval of length h is proportional to h. In notation, P(one success) = \(\lambda h\text{.}\)
- The probability of two or more successes in a sufficiently small interval is essentially 0.
You should presume these assumptions implicitly for the distributions discussed in this chapter.
In this chapter, you will investigate the following distributions:
- Poisson - the interval is fixed and X measures the variable number of successes.
- Exponential - the number of successes is fixed--at 1--and X measures the variable interval length needed to get that success.
- Gamma - the number of successes is fixed and X measures the variable interval needed to get the desired number of successes.