Applied Statistics and Probability for Engineers

3-9 POISSON DISTRIBUTION 91

Historically, the term processhas been used to suggest the observation of a system over

time. In our example with the copper wire, we showed that the Poisson distribution could

also apply to intervals such as lengths. Figure 3-14 provides graphs of selected Poisson

distributions.

It is important to use consistent unitsin the calculation of probabilities, means, and vari-

ances involving Poisson random variables. The following example illustrates unit conversions.

For example, if the

average number of flaws per millimeter of wire is 3.4, then the

average number of flaws in 10 millimeters of wire is 34, and the

average number of flaws in 100 millimeters of wire is 340.

If a Poisson random variable represents the number of counts in some interval, the mean of the

random variable must equal the expected number of counts in the same length of interval.

0

0.2

0.6

λ

0.1

0.4

1.0

0

135791124 81012

0.8

f(x)

0

0.2

0.6

λ

0.4

1.0

0

2

135791124 81012

0.8

0.2

0.6

λ

0.4

1.0

0

5

0.8

6

x

(a)

6

x

(b)

f(x)

f(x)

Figure 3-14 Poisson distributions for selected values of the parameters.

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