A communications satellite is designed to have a mean time to failure (MTF) of five years. If the actual time to failure is a random variable that is exponentially distributed, find: a) The probability that the satellite will fail sooner than five years. b) The probability that the satellite, will survive for ten years or more. c) The probability that the satellite will fail during the sixth year.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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A communications satellite is designed to have a mean time to failure
(MTF) of five years. If the actual time to failure is a random variable that
is exponentially distributed, find:
a) The probability that the satellite will fail sooner than five years.
b) The probability that the satellite, will survive for ten years or more.
c) The probability that the satellite will fail during the sixth year.
Transcribed Image Text:A communications satellite is designed to have a mean time to failure (MTF) of five years. If the actual time to failure is a random variable that is exponentially distributed, find: a) The probability that the satellite will fail sooner than five years. b) The probability that the satellite, will survive for ten years or more. c) The probability that the satellite will fail during the sixth year.
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