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 maybe described in terms of its hazard functionh(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 identifythe distribution of T. Hence show that the mean lifetime of thesebatteries is approximately 12.53 months, and calculate the variance ofthe lifetime.(c) What proportion of batteries last for less than six months?

The lifetime T of the battery of a calculator has a hazard function given by: ht=1100t, t≥0…

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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

A First Course in Probability (10th Edition)

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Question

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?

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