Calculus for Biologists Lab
Math 1180-002
Spring 2012
Assignment #10 - The Poisson Process and Distribution
Report due date: Tuesday, April 3, 2012 at 9 a.m.
? Please number your responses to each problem in your write-up.
1. Include Plot 10.1 from lab 10.
(a) How many attacks occurred within the 24-hour period?
(b) How does the number of attacks near the earlier hours of the simulation compare to the number of
attacks nearer the end of the simulation?
(c) During which hours were there no attacks?
(d) During which hour(s) did the largest number of attacks occur?
(e) Given the intervals in which there were multiple attacks, were these more likely to occur close together
or farther apart?
2. Include Plot 10.2 from lab 10.
(a)
i. In your simulation, what is the mode of the number of attacks in any given hour, and what is the
corresponding probability?
ii. What is the mode of the number of attacks in the Poisson distribution, and what is the corresponding probability?
iii. How do these results compare?
(b)
i. Use the total number of attacks to estimate the average number of attacks in an hour, based on
your simulation results.
ii. What is the expected number of attacks in an hour predicted by the Poisson distribution?
iii. Compare these expected values.
(c) Describe in detail the similarities and differences between the two distributions.
3. Include Plot 10.3 from lab 10.
(a) Describe the similarities and differences of the plots for each p value.
(b) Give a (mathematical) explanation for the differences you observe. You may want to think about the
probability functions, expectations and variances of each distribution.
(c) Compare the behavior of the binomial and Poisson distributions when p = 0.01.
(d) Based on your observations, name a condition under which the Poisson distribution can be a good
approximation of the binomial distribution.
(e) How do you think these distributions would compare if only 5 pigs (and 10 eyes) were checked for
injuries instead?
? Save your report as a .pdf file and upload it to Blackboard.
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