Revisit Application Problem 8.29 above and now consider that a married cou- ple, both of whom are carriers, lives in a country where there is no health care coverage, so that each family must cover its own health care costs. The couple, not knowing that that are both carriers, proceed to have 8 children. A child with the sickle-cell disease will periodically experience episodes called "crises" that will re- quire hospitalization and medication for the symptoms (there are no cures yet for the disease). Suppose that it costs the equivalent of US$2,000 a year in general hospital costs and medication to treat a child with the disease.
(i) What annual sickle-cell disease-related medical cost can this family expect to incur?
(ii) If these "crisis" episodes occur infrequently at an average rate of 1.5 per year in this country (3 every two years), and these occurrences are well-modeled as a Poisson-distributed random variable, what is the probability that this family will have to endure a total of 3 crisis episodes in one year? Note that only a child with the disease can have a "crisis" episode. (Hint: See Exercise 8.21.)