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Exercise for April 19, 2008
November 2000 Course 1 Examination, Problem No. 34, also Study Note P-09-07,
Problem No. 29
The number of days that elapse between the beginning of a calendar year and the moment
a high-risk driver is involved in an accident is exponentially distributed. An insurance
company expects that 30% of high-risk drivers will be involved in an accident during the
first 50 days of a calendar year. What portion of high-risk drivers are expected to be
involved in an accident during the first 80 days of a calendar year?
A. 0.15
B. 0.34
C. 0.43
D. 0.57
E. 0.66
Solution.
Let T be the number of days that elapse before a high-risk driver is involved in an
accident. We know that T is exponentially distributed with unknown parameter !. We
are also given that
0.3 = Pr (T ! 50 ) = 1 " e"50 # .
Therefore, e!50 " = 0.7 and
ln 0.7
!="
.
50
It follows that
Pr (T ! 80 ) = 1 " e
Answer C.
"80 #
= 1" e
80
$ln 0.7
50
= 1 " 0.7
80
50
= 0.435.
© Copyright 2004-2008 by Krzysztof Ostaszewski.
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Exercises from the past actuarial examinations are copyrighted by the Society of
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