The UN is going to build a small clinic in a remote village in Africa to deal with the recent outbreak of a disease. The probability of having the disease is 0.35. The doctors can perform medical exams on 5 people every day. Those who are affected need to be hospitalized and treated for one day. The doctors need to decide whether to build a two-bed clinic or a three-bed clinic. The cost of a two-bed clinic is $400 per day, whereas the cost of a three-bed clinic is$570 per day. If they build a two-bed clinic, they can treat up to two patients (who are aff ected by the disease) in the clinic, and send the remaining possible patients (note that they can have up to 5 patients everyday) to the nearest hospital. If they build a three-bed clinic, they can treat up to three people in the clinic and send the rest of possible patients to the hospital. The cost of sending patients to the hospital (i.e., ambulance, fuel, paramedics, driver...) is \$600 per patient. We are assuming that the patients who are treated in the clinic will be released by the next day so the beds will be free at the beginning of each day, and the quality and risk of treatment is the same as that of the hospital. Assume that the number of a ffected people out 5 people examined has a Binomial(5, 0.35) distribution and use the expected loss principle to decide which option is better: two-bed clinic or three-bed clinic.

2. Well, I'm not quite sure if I'm right (haven't got any statistic books in front of me to check it out), but lets try anyway.

Given this information, we can conclude that the probability that 0 are going to be sick is 11,603%, that 1 is going to be sick is 31,239%, that 2 are going to be sick is 33,642%, that 3 are going to be sick is 18,115%, that 4 are going to be sick is 4,877% and that 5 are going to be sick is 0,525%.

Now, consider the following two scenarios.

1) If we build two beds then:

• Expected travel cost if 3 are sick (means that 1 is going to the hospital) is going to be 1*18,115%*600 = 108,6881.
• Expected travel cost if 4 are sick (means that 2 are going to the hospital) is going to be 2*4,877%*600 = 58,524.
• Expected travel cost if 5 are sick (means that 3 are going to the hospital) is going to be 3*0,525%*600 = 9,4539.

The sum of this plus the daily cost of running the two bed clinic will then equal to 576,67.

2) If we build three beds then:

• Expected travel cost if 4 are sick is 29,26
• Expected travel cost if 5 are sick is 6,30.

The sum of this plus the daily cost of running the three bed clinic will then equal to 605,56.

Hence, it is cheaper to build just the two bed clinic.