where can I find simple problems dealing with the poisson distribution?

Question

with answers and also examples of how they were done

Answer 1

It's a three step process:
1. type 'poisson distribution' into a search engine
2. get the same 300+ hits that I just got
3. wade through them until you find what you want ☺

Doug

Answer 2

Go here: http://www.umass.edu/wsp/statistics/lessons/poisson/

Some of the problems found:

Isolated Events

It has been observed that the average number of traffic accidents on the Hollywood Freeway between 7 and 8 PM on Tuesday mornings is 1 per hour. What is the chance that there will be 2 accidents on the Freeway, on some specified Tuesday morning?

Answer. The basic rate is r = 1 (in hour units), and we need to find the chance of 2 per hour. Since the rate is simple, it will be included in the Poisson Table. Reading down the r = 1 column, we come to the p(2) row, and there we find that the corresponding probability of 2 accidents is 0.1839, or a little greater than 1 chance in 5. It's not unlikely.

Proportions

Coliform bacteria are randomly distributed in a certain Arizona river at an average concentration of 1 per 20cc of water. If we draw from the river a test tube containing 10cc of water, what is the chance that the sample contains exactly 2 coliform bacteria?

Answer. Our unit of observation is 10cc. If the concentration (r) is 1 per 20cc, it is also 0.5 per 10cc, and that becomes the relevant rate. We can then read off all probabilities from the r = 0.5 column of the Poisson Table. For the specific value of p(2), the table supplies the answer 0.0758, or about 1 chance in 13. Not common, but not out of the question either.

Arrivals

The switchboard in a small Denver law office gets an average of 2.5 incoming phonecalls during the noon hour on Thursdays. Staffing is reduced accordingly; people are allowed to go out for lunch in rotation. Experience shows that the assigned levels are adequate to handle a high of 5 calls during that hour. What is the chance of 6 calls being received in the noon hour, some particular Thursday, and thus missing an important call?

Answer. This result too is easily read off the Poisson Table, from the p(6) row of the r = 2.5 column. The answer is p(6) = 0.0278, or about 1 chance in 36. Roughly 1 per month. How acceptable that is will depend on how cranky the firm's clients are, and the firm itself is in the best position to make that judgement.

Answer 3

In any basic math statistics or probability book -- or Google it. There are many online references/statistics tutorials/courses that will discuss the Poisson Distribution.