Science:Math Exam Resources/Courses/MATH103/April 2017/Question 09 (d)

MATH103 April 2017

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Question 09 (d)
The probability density function (pdf ) for the mortality of a jellyfish (Turritopsis dohrnii), $p(x)$, at age $x$ is given by $p(x)={\frac {2}{\pi }}\cdot {\frac {1}{1+x^{2}}},$ for $0\leq x<\infty$. (d) Consider a large colony of Turritopsis dohrnii jellyfish. After how many years do we expect that half of the animals of the original colony have died?

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Assume that all jellyfish in the original colony are of the same age (the age being equal to zero years). Use the fact that the colony of jellyfish is large, and consider part b) of this question.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Assume that time is measured in years. Because the colony is large (and since, at the beginning, all jellyfish in the original colony are zero years old) the time at which half of them will die equals to the median mortality of the jellyfish, which, by part b), equals $\color {blue}1{\text{ year}}$