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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. page 5 of 7

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. page 5 of 7

A First Course in Probability (10th Edition)
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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Question is about renewal processes in continuous time (please see attached)

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, t20. page 5 of 7 (a) Find the survivor function Q(t). (b) Write down the c.d.f. of T, and use Table 9 in the Handbook to identify the distribution of T. Hence show that the mean lifetime of these batteries is approximately 12.53 months, and calculate the variance of the lifetime. (c) What proportion of batteries last for less than six months?
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)=t, t20. page 5 of 7 (a) Find the survivor function Q(t). (b) Write down the c.d.f. of T, and use Table 9 in the Handbook to identify the distribution of T. Hence show that the mean lifetime of these batteries is approximately 12.53 months, and calculate the variance of the lifetime. (c) What proportion of batteries last for less than six months?
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