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All that is known about a certain stationary population of insects is that the age-specific death rate is given by the formula 2x h(x) = 100-² where x is measured in days. 0≤x≤ 10, 1. Draw a sketch of h(x), and hence describe the way in which death rates change with age. 2. Find Q(x), the life table function for insects in this population. 3. Find eo, the expectation of life at birth.

All that is known about a certain stationary population of insects is that the age-specific death rate is given by the formula 2x h(x) = 100-² where x is measured in days. 0≤x≤ 10, 1. Draw a sketch of h(x), and hence describe the way in which death rates change with age. 2. Find Q(x), the life table function for insects in this population. 3. Find eo, the expectation of life at birth.

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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All that is known about a certain stationary population of insects is that the age-specific death rate is given by the formula 2x h(x) = 100x² where x is measured in days. 0≤x≤ 10, 1. Draw a sketch of h(x), and hence describe the way in which death rates change with age. 2. Find Q(x), the life table function for insects in this population. 3. Find eo, the expectation of life at birth.
Transcribed Image Text:All that is known about a certain stationary population of insects is that the age-specific death rate is given by the formula 2x h(x) = 100x² where x is measured in days. 0≤x≤ 10, 1. Draw a sketch of h(x), and hence describe the way in which death rates change with age. 2. Find Q(x), the life table function for insects in this population. 3. Find eo, the expectation of life at birth.
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(d) At any time, find the mean age of insects in the population.

 

(e) Sketch g(x), the p.d.f. of the age distribution of insects in the population.

 

(f) No calculations are required for this part of the question.
Now suppose that a population with the life table function Q(x) that
you obtained in part (b) is stable but not stationary. Describe briefly
how the age distribution of the population would differ from that of a
stationary population with the same life table function if the population
is (i) growing, (ii) declining. Draw rough sketches to show what the
p.d.f. of the age distribution might look like in each case.

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