Can you recognize a Poisson situation? The Poisson distribution has 4 main characteristics:

1. An event of interest occurs randomly over time or space.
2. The average arrive rate remains constant.
3. The arrivals are independent of each other.
4. The random variable (X) is the number of events within an observed time interval.

6.40 (a) Why might the number of yavvns per minute by students in a warm classroom not be a Poisson event? (1}) Give two additional examples of events per unit of time that might violate the assumptions of the Poisson model, and explain why. Recognizing Poisson Applications Can you recognize a Poisson situation? The Poison detribution has four main characteristics. . An event of interest occurs randomly over line of space. The merge arrived nile lif remains curslant. " The arrivals are independent of each other. The random variable (J) is the number of events within an observed time interval, Ask yourself if the four characteristics alame make sense in the fullowing csamples. In the bed week, how many credit card applications did you receive by mail? In the kid week, how many checks did you write? In the bed week, how many e-mail viruses did your firewall deflect? It mary be a Poisson process, even if you don't know the mean (i). In business applications, the value of A would have to be calimuted from experience, but in this clepler a will be given. Using the Poisson Formula Table 6. Il shores the probabilities for each value of X. The probabilities for individual fendues can be calculated by inserting 1 - 1.7 into the Poison PDF or by using Excel's Poisson function -POISSON.DIST(s, 2, cumulative) where cumulative is 0 (if you wanta PDF) or Iff you winl : CDF). Table Ull Probability Distribution for A = 1.7 0 1827 .3106 2640 .3571 .1496 JOER 0635 9704 LA 0051 9996 0303 9959 LOODO POf Farmvir 1827 - POLSON BIRTH, 1.1, 0) -.3106 - POISSON BET I, I,T.D) 17 -.2649 - POISSON DISTIZ, 1.T.D) - 0 - POISSON DISTIE 1, T, D) POX -9)m - DHHHI - POISSON BETIS, 1.T. Poison probabilities must sum to I (except due to manding) as with any discTele probability distribution. Beyond I- 9, the probabilities are below .DODI. Graphs of the PDF and CDF are shown in 5 Figure 6.12. The most likely event is one arrival (probability 3106, or a 31.1 percent cleancek, although two arrival are almost as likely (probability .264], or a 264 percent chance]. This PDF would help the credit union schedule its tellers fur the Thursday morning work shill. Figure 8.12 Poisson POP and CoF for A = 1.7 30 .10 30 30