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Spring 2003
1.
Alamo Rental Car Company
Note: some of you have a slightly incorrect version of this problem as there was a
change in the numbers given for the # of losses per month per car.
This was
apparently due to some random event in cyber space that caused a number to
appear twice.
The data below is correct.
You will not be penalized in grading if
you received the incorrect version as long as you did the problem correctly.
a.
Random variable # of losses per car per month.
b.
Mean: (0)(.05) + (1)(.25) + (2)(.30) + (3)(.05) + (4)
(.10) + (5)(.25) = 2.65 losses per car per month
c.
Number
Mean
Diff.
From
Mean
Diff.
Squared
Prob.
Diff.
Squared
times
prob.
0
2.65
2.65
7.02
.05
.351
1
2.65
1.65
2.72
.25
.68
2
2.65
.65
.42
.30
.126
3
2.65
.35
.12
.05
.006
4
2.65
1.35
1.82
.10
.182
5
2.65
2.35
5.52
.25
1.38
Variance =
2.725
Standard Deviation is the square root of the variance: S.D.= 1.65
Coefficient of variation = standard deviation / mean =1.65/ 2.65= .62
d.
The units of measure are :
Mean: losses per car per month
Variance: (losses per car per month)
2
Std deviation: losses per car per month
Coefficient of Variation: unitless or a percentage
e.
The losses are always $1200.
Therefore severity is
NOT random.
The expected total loss per car per month is 2.65*1200= $3180.
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This note was uploaded on 04/28/2011 for the course RMI 2901 taught by Professor Manaka during the Spring '11 term at Temple.
 Spring '11
 MANAKA

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