The lifetime T (in months) of the battery in a certain type of calculator may be described in terms of its hazard function h(t)=t, t≥ 0. Whenever a battery fails, it is immediately replaced. Michael has a calculator containing one of these batteries. Suppose that at some time when the calculator is quite old, Michael gives it to his brother Robert. (f) Calculate the mean total lifetime of the battery in the calculator when Michael gives the calculator to Robert. Hence calculate the mean residual lifetime of this battery. (g) If Robert keeps the calculator for three years, how many times should he expect to replace the battery in that time?
The lifetime T (in months) of the battery in a certain type of calculator may be described in terms of its hazard function h(t)=t, t≥ 0. Whenever a battery fails, it is immediately replaced. Michael has a calculator containing one of these batteries. Suppose that at some time when the calculator is quite old, Michael gives it to his brother Robert. (f) Calculate the mean total lifetime of the battery in the calculator when Michael gives the calculator to Robert. Hence calculate the mean residual lifetime of this battery. (g) If Robert keeps the calculator for three years, how many times should he expect to replace the battery in that time?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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:The lifetime T (in months) of the battery in a certain type of calculator may
be described in terms of its hazard function
h(t) = ot, t≥ 0.
Whenever a battery fails, it is immediately replaced. Michael has a
calculator containing one of these batteries. Suppose that at some time when
the calculator is quite old, Michael gives it to his brother Robert.
(f) Calculate the mean total lifetime of the battery in the calculator when
Michael gives the calculator to Robert. Hence calculate the mean
residual lifetime of this battery.
(g) If Robert keeps the calculator for three years, how many times should
he expect to replace the battery in that time?
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