STAT 400
Examples for 02/09/2011
Spring 2011
5.
Management of an airline knows that 0.5% of the airline’s passengers lose their
luggage on domestic flights.
Management also know that the average value
claimed for a lost piece of luggage on domestic flights is $600.
The company
is considering increasing fares by an appropriate amount to cover expected
compensation to passengers who lose their luggage.
By how much should the
airline increase fares?
Let X denote the compensation to a passenger due to lost luggage.
Then X has the following probability distribution:
x
f
(x)
x
⋅
f
(x)
$
0
0.995
0
$
600
0.005
3
1.00
$
3
The average compensation to each passenger due to lost luggage is $
3.
The airline should increase fares by $
3
.
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Suppose an insurance policy reimburses a loss up to a benefit limit of
C
and has
a deductible of
d
.
If the policyholder’s loss is
X
,
then
Benefit Paid
=
+
≥
+
<
≤

<
d
x
d
x
d
d
x
d
x
C
C
C
0
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6.
A grocer has shelf space for two units of a highly perishable item that must be
disposed of at the end of the day if it is not sold.
Each unit costs $1.70 and sells
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 Spring '08
 Kim
 $10, $15, $0, $1.70, $3.50

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