Calculus for Biologists Lab
Math 1180-002
Spring 2012
Assignment #8 - Pathogen exposure and illness
Report due date: Tuesday, March 20, 2012 at 9 a.m.
? Please number your responses to each problem in your write-up.
1. Include Plot 8.1 from lab 8. Use the results in your figure to answer the following questions for
(a) the immune-compromised group
(b) the elementary school teachers
i. What level of pathogen exposure is this group more likely to experience?
ii. Why does this exposure level make sense for this group?
iii. Is an individual in this group more or less likely to be sick?
iv. Why do you think this status might be more likely for this group?
2. Include Plot 8.2 from lab 8.
Use the results in your figure to answer the following questions for
(a) the immune-compromised group
(b) the elementary school teachers
i. Give a detailed description (in words) of Pr(L|S = 0). Specifically, describe how being healthy
indicates how much pathogen exposure one received.
ii. Give a detailed description (in words) of Pr(L|S = 1). Specifically, describe how being sick
indicates how much pathogen exposure one received.
(c) Can a non-sick immune-compromised person have been exposed to high pathogen levels, based on
your data? Use the appropriate histogram to explain.
(d) Can a sick teacher have been exposed to low pathogen levels? Use the appropriate histogram to
explain.
3. Include Plot 8.3 from lab 8.
(a) If an immune-compromised person experiences high pathogen exposure, what is the probability of
sickness?
(b) If a teacher experiences high pathogen exposure, what is the probability of sickness?
(c) Under what conditions do the immune-compromised and teachers behave similarly?
4. What interesting aspects of the marginal distributions can be explained by the conditional probabilities?
Address each group separately.
5. What interesting aspects of the conditional probabilities are absent in the marginal distribution? Address
each group separately.
6. (a) Use the marginal probability distribution in Plot 8.1 and the expected values from lab 8 to calculate
the standard deviations of L and S for the immune-compromised individuals.
(b) Do the same for the group of elementary school teachers.
7. Using your results from the previous problem, calculate the correlation between L and S for the immunecompromised group, according the following formula:
ρL,S =
Cov
,
σL σS
where σL and σS are standard deviations of the marginal distribution.
8. Answer the following questions for
(a) the immune-compromised group
(b) the elementary school teachers
i. Is there a positive, negative or zero correlation between pathogen exposure and sickness in this
group?
ii. Is this correlation weak (closer to zero) or strong (closer to 1 or -1)?
iii. What group characteristics may explain this type of correlation?
? Save your report as a .pdf file and upload it to Blackboard.
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