The life table function for the members of a stationary animal population is given by Q(x)=1- 0≤x≤k, where x is measured in years. (a) Show that the mean lifetime for members of this population is 2k/3. (b) Find the mean age of the members of the population at any time. (c) (i) What proportion of members of the population live for longer than k/2 years? (ii) At any time, what proportion of members of the population are more than k/2 years old?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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The life table function for the members of a stationary animal
population is given by
Q(x)=1-
0≤x≤k,
where x is measured in years.
(a) Show that the mean lifetime for members of this population is
2k/3.
(b) Find the mean age of the members of the population at any time.
(c) (i) What proportion of members of the population live for longer
than k/2 years?
(ii)
At any time, what proportion of members of the population
are more than k/2 years old?
Transcribed Image Text:The life table function for the members of a stationary animal population is given by Q(x)=1- 0≤x≤k, where x is measured in years. (a) Show that the mean lifetime for members of this population is 2k/3. (b) Find the mean age of the members of the population at any time. (c) (i) What proportion of members of the population live for longer than k/2 years? (ii) At any time, what proportion of members of the population are more than k/2 years old?
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