Suppose the lifetime in years T of a component of a solar heating system is uniformly distributed and may be anything between 0 and 25 years, i.e. T~ U(0,25). (a) Find the survivor function (t) for the component and the mean value of T. (b) Find the hazard function h(t) for these types of component and draw a sketch of h(t). Use your sketch of the hazard function to decide whether such components are NBU, NWU or neither. Assume that at some point in the future the solar heating system is replaced and this component is retained and installed into the new system. (c) Find the probability that this component (i) will need replacement within five years from the time it was installed into the new system, and (ii) will last longer than ten years from the time it was installed into the new system.
Suppose the lifetime in years T of a component of a solar heating system is uniformly distributed and may be anything between 0 and 25 years, i.e. T~ U(0,25). (a) Find the survivor function (t) for the component and the mean value of T. (b) Find the hazard function h(t) for these types of component and draw a sketch of h(t). Use your sketch of the hazard function to decide whether such components are NBU, NWU or neither. Assume that at some point in the future the solar heating system is replaced and this component is retained and installed into the new system. (c) Find the probability that this component (i) will need replacement within five years from the time it was installed into the new system, and (ii) will last longer than ten years from the time it was installed into the new system.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Suppose the lifetime in years T of a component of a solar heating
system is uniformly distributed and may be anything between 0
and 25 years, i.e. T~ U(0,25).
(a) Find the survivor function Q(t) for the component and the mean
value of T.
(b)
Find the hazard function h(t) for these types of component and
draw a sketch of h(t). Use your sketch of the hazard function to
decide whether such components are NBU, NWU or neither.
Assume that at some point in the future the solar heating system is
replaced and this component is retained and installed into the new
system.
(c) Find the probability that this component (i) will need replacement
within five years from the time it was installed into the new
system, and (ii) will last longer than ten years from the time it
was installed into the new system.
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