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Chapter 5: Problem 47

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

Short Answer

Expert verified
The conditions for applying a Poisson probability distribution are: 1) Independence of events, 2) A constant average rate of event occurrence, 3) The ability for theoretically infinite occurrences in a small interval (though the probability is nearly zero), 4) No simultaneous events.

Step by step solution

01

Condition 1: Independence

The first condition is that the events are independent of each other. This means the occurrence of one event does not affect the probability of another event occurring.
02

Condition 2: Constant Average Rate

The second condition is that the average rate (lambda, \(\lambda\)) of event occurrence is constant. The rate at which events occur is consistent over time.
03

Condition 3: Theoretically Infinite Occurrences

The third condition is that, theoretically, in an infinitesimally small interval, more than one event can occur. However, the probability of more than one occurrence is virtually zero.
04

Condition 4: No Simultaneous Occurrences

The fourth condition is that no two events occur at exactly the same instant.

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Most popular questions from this chapter

A review of emergency room records at rural Millard Fellmore Memorial Hospital was performed to determine the probability distribution of the number of patients entering the emergency room during a 1 -hour period. The following table lists this probability distribution. $$ \begin{array}{l|ccccccc} \hline \begin{array}{l} \text { Patients } \\ \text { per hour } \end{array} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Probability } & .2725 & .3543 & .2303 & .0998 & .0324 & .0084 & .0023 \\ \hline \end{array} $$ a. Make a histogram for this probability distribution. b. Determine the probability that the number of patients entering the emergency room during a randomly selected 1 -hour period is i. 2 or more ii. exactly 5 iii. fewer than 3 iv. at most 1

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