The lifetime T (in months) of the battery in a certain type of calculator may be described in terms of its hazard functi
Posted: Thu May 05, 2022 9:04 pm
- The Lifetime T In Months Of The Battery In A Certain Type Of Calculator May Be Described In Terms Of Its Hazard Functi 1 (236.29 KiB) Viewed 28 times
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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. (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? (d) Find the median lifetime of these batteries. (e) Decide whether the batteries are NBU, NWU or neither, justifying your answer. 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?