Problem 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 PA- the Northeast (NE) and the Southwest (SW).
Assume that the following information is based on the past 10 years of data and you are projecting for the year 2015.
The CAP has the following data for the number of accidents per airplane in the NE Region.
|
# of accidents per airplane per year
|
Probability of having this # of accidents
|
|
0
|
0.60
|
|
1
|
0.25
|
|
2
|
0.10
|
|
3
|
?
|
a) What is the random variable illustrated here?
b) What is the probability of an airplane having 3 accidents in a year?
c) Calculate the expected number of accidents per airplane per year for the NE Region. What are the units of measurement?
d) The NE Region has 500 airplanes dispersed at various general aviation airports throughout the region. What is the expected number of accidents for all airplanes in the NE Region?
e) CAP has calculated the variance for the NE Region frequency distribution to be equal to 0.74. Since you want to be sure you are using correct numbers in your evaluation, prove that CAP calculated the correct variance for frequency for the NE Region. Show all work!
Round each calculation to 4 decimal places. You must use this validated variance (0.74) for all further calculations.
Problem 2 - You have calculated the following information related to the number of accidents per airplane for the SW Region. You have had someone else check your calculations and are sure that these numbers are valid. The SW Region has 1000 planes.
Mean = 1.1
Variance = 0.81
Suppose that each region has a separate property insurance contract and that you are going to negotiate with the insurance company about insurance premiums for the NE and SW Regions.
a) Which region faces the most risk and why? Show all calculations and explain your numerical results.
Problem 3 - On Thursday, Jenny is expecting to receive one package of goodies from her online shopping spree. This package contains $200 worth of clothing. Based on her past experience with the delivery service, Jenny estimates that this package has a 20% of chance of being lost in transit.
a) What is the mutually exclusive event in this case?
b) Derive the probability distribution for total losses. Make sure that you label your table correctly. Hint: consider the random variable here to be the dollar amount of losses.
c) Derive the probability distribution for total dollar amount losses of the two packages. In this case, you need to consider all the possible outcomes in terms of dollar amount of losses, recognizing that Jenny now is expecting two packages.
Attachment:- Assignment.rar