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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 reproduce)? 1