In the preceding chapter we have introduced the Poisson process from two different viewpoints. According to Definition 3.2.2 the Poisson process has stationary independent increments and the probability that an event takes place for a small interval h is λh, where the proportional constant λ is the parameter of the process. Furthermore, according to Definition 3.3.2 the Poisson process is a renewal process in which the interarrival times are independent and identically distributed exponentially with the mean 1/λ. Figure 4.1.1 shows two realizations of the Poisson process from these two viewpoints.
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