-1-
Stat 231 Exam I
October 6, 1997
Professor Vardeman
1
.
The random variable
the number of hours till failure of a WD disk drive
\ œ
is described using an exponential distribution with mean 15,000 hours.
(a)
Evaluate the probability that a given drive lasts at least 20,000 hours.
(b)
A new computer network has 10 of these drives installed on computers in the network.
Use
your answer to (a) and an assumption of independence of the 10 drive lifetimes and evaluate the
probability that at least 9 of these drives are failure-free through 20,000 hours.
No need to
simplify.
(If you could not do (a) use the incorrect value of .17.)
(c)
A WD warranty program pays customers for early failure of drives of this type according to
the following schedule:
Failure in the first 10,000 hours produces a payment of $300
Failure at
hours (10,000
20,000) produces a payment of $300
2
B
B
Ð
Ñ
B
"!ß!!!
Failure at
hours with
20,000 produces no payment
B
B
Set up (but do not attempt to evaluate) an expression for the mean warranty payment under this
plan.
(This is
for an appropriate function
.)
E
2Ð\Ñ
2

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