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Chapter 5: Problem 69

What are the conditions that must be satisfied to apply the Poisson probability distribution?

Short Answer

Expert verified
The conditions that must be satisfied to apply the Poisson probability distribution are: Independence of events, events occur at a constant average rate, the events are non-overlapping, and the probability of two or more events occurring in a given interval of time or space must be virtually zero.

Step by step solution

01

Condition 1: Independence

The first condition is that the events must be independent. This means that the occurrence of one event does not affect the probability of another event happening. For example, if an event is about the arrival of customers, the arrival of one customer should not influence the arrival of the next.
02

Condition 2: Occurrence rate

The rate at which events occur is constant. This means that the events are happening at a stable average rate for the specified period of time or space.
03

Condition 3: Non-overlapping events

Any two events cannot occur at the exact same instant, the events are non-overlapping. This means that only one event can happen at a given moment.
04

Condition 4: Arbitrary Count

The probability of the occurrence of two or more events in a short interval or small region must be virtually zero. That is, only one event can occur in a given interval of time or space.

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