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THE UNIVERSITY OF IOWA
22S:175
H.W. Set #3 Due at the
beginning
of class on Monday, February 7, 2011
Write legibly.
Show your steps.
Explain your reasoning.
Simplify your answers.
Each question is worth 10 points
1. Hogg, McKean & Craig (2005)
Intro to Math Stat
, 6
th
edition, page 157 #3.3.5.
Remarks
: (i) This result can also be found in
Actuarial Mathematics
and in
Introduction
to
Probability Models
.
(ii) If you use the antiderivative in the Hint, you should first
show that it is indeed an antiderivative; otherwise, points will be deducted.
2. (An old SOA exam question) A Mars probe has n batteries. Once a battery is activated,
its future lifetime is
exponential
with mean
years.
The first battery is activated when the probe lands on Mars. The second battery is
activated when the first fails. The third battery is activated when the second fails, and
so on.
Battery lifetimes after activation are independent.
The probe transmits data
until all n batteries have failed.
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 Spring '08
 Tang,Q

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