Microsoft Office Tutorials and References
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Exhibit 8.10 Auto arrival sampling area of brain
Now, let us examine in detail how we simulate Poisson arrivals. Recall how we
introduced the RAND() function in Exhibit 8.2. We generated uniformly distributed
random numbers and then assigned an outcome value (a color) to the random num-
ber depending on its value. If the random number value was between 0 and 0.3, a
Red was returned; if between 0.3 and 0.6, a White was returned; if between 0.6 and
1.0 a Blue was returned. We will use the table of cumulative Poisson probability
values in a similar fashion. Although we did not mention the cumulative nature of
the comparison values before, the IF() used cumulative values to determine the col-
ors for our sampling. To build a cumulative Poisson probability table, we will use
the internal Excel cell function, POISSON(x, mean, cumulative) . Then we will
use the table as the basis for sampling the number of arrivals for a unit of time. The
arguments of the function, x and mean , are values that the user provides. By placing
the term true in the third argument of the function, cumulative , a cumulative value
will be returned; that is, the value x
=
3 will return the probability of 0, 1, 2, and 3
arrivals for the Poisson distribution.
Now, consider the table in Exhibit 8.10 associated with the average arrival rate,
λ
, of 4 (in column D). In this exhibit we consider the arrival of autos at a repair
facility in two distinct time periods: 5:00–7:00 and 7:00–9:00. The arrival rate of
the later time period is 2; thus, on average more cars arrive earlier rather than later.
Beginning in cell D7 and continuing to D19, the table represents the successive
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