MATH 3900, Spring 2009 Homework 10 Due 04/10/09

MATH 3900, Spring 2009
Homework 10
Due 04/10/09
1. Finish example that we considered in class: a protein can bind in any
given second with probability 0.7. You are observing it for 5 seconds and record
the total number of proteins bound. Find the (binomial) distribution for the
number of bound proteins, illustrate it with a histogram, compute the average
number of bound proteins you expect to see in many such experiments. Repeat
for p = 0.5, p = 0.2.
2. In the model for disease spread in a family, consider the following conditions: A family consists of 6 people, p = 0.2, S1 = 4, I1 = 2.
a) Find diribution of S2 . Illustrate it with a histogram. What is average number
of still-healhy people on the second day of the disease?
b) (computing) Simulate a course of disease in 20 such families (until the disease runs out). In each one record the total number of people affected.
c) (computing) Repeat b) with p = 0.4 and p = 0.6. If you are a healh care
official, you are dealing with a serious disease that has p = 0.6 and you have
an expensive drug that can reduce infectivity p to 0.4. Does it make sense to
introduce it? What about a drug that reduces p to 0.2?
3. In the sickle cell anemia model, assume R = .2, T = 0.1, S = 0.4.
a)What will happen to disease in this population in the long run (use cobwebbing)?
b) How will the model change if individuals with bb genotype are sterile (cannot