risk

1. The Civil Air Patrol (CAP) owns airplanes used for search and rescue missions. In the course of their activities, CAP sustains losses in the form of property damages to their airplanes. Assume that the CAP covers two major regions in Pennsylvania– the Northeast (NE) and the Southwest (SW). The NE Region has 500 planes. The CAP has the following data for the number of accidents per airplane in the NE Region.

a. What is the random variable illustrated here?

Number of accidents per airplane per year is the random variable.

b. Derive the probability distribution based on this data. Be careful to label 
exactly what you are defining as the probability distribution.

481+13+6 =500

There are 96.2% of airplanes having 0 accident per year.

There are 2.6% of airplanes having 1 accident per year.

There are 1.2% of airplanes having 2 accidents per year.

c. Calculate the expected value of frequency per airplane. Round your calculation to 4 decimal places. What are the units of measurement?

Expected value of frequency= 25/500 = 0.0500

The unit of measurement is expected value of the number of accident; it is the measure of central tendency. The expected value of frequency which is there are .05 accidents per airplane.

d. CAP has calculated the variance for the NE Region frequency distribution to be equal to 0.0715. Since you want to be sure you are using correct numbers in your evaluation, prove that CAP calculated the correct variance for frequency. Show all work! Round each calculation to 4 decimal places. You must use this validated variance (0.0715) for all further calculations. What are the units of measurement?

Mean=(0)(.962)+(1)(.026)+(2)(.012)=. 05

Variance=. 0024+. 0235+. 0456=. 0715

The units of measurements are number of airplanes and number of accidents; variance is the measure of disposition.

2. The CAP also has the following data for the number of accidents per airplane in the SW Region. The SW Region has 600 planes.

You have had someone else check your calculations and are sure that these numbers are valid.

Mean =0.055

Variance =0.082

Which region is riskier, NE Region or SW Region? And why? Show all calculations and explain your numerical results.

Standard deviation for NE = (.0715)^(1/2) = .2674

Standard deviation for SW = (.082)^(1/2) = .2864

Coefficient of variance for NE = .2674/. 05 = 5.348

Coefficient of variance for SW = .2864/ .055 =5.2073

NE region faces more risk, because they have a higher coefficient of variance. Coefficient of variance = Standard deviation / mean

3. For the NE Region, assume initially that when accidents do occur, they are non- random and equal to $25,000.

a. Calculate the expected loss per airplane for NE Region.

Expected loss per airplane = E (f)*E (S) = (.05)*25,000 =1,250

b. Calculate the expected loss for ALL airplanes for NE Region.

(1,250)*(500)=625,000

4. Now based on the report in NE Region, CAP has constructed the following information related to the dollar amount of losses for 25 reported accidents.

a. Calculate the expected value of severity per airplane.

E (S) = 688,550/25 = 27,542

b. Calculated the expected loss per airplane.

Expected loss per airplane= E (f)*E (S)= (.05)*(27,542)=1,377.1