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

The probability density function (pdf ) for the mortality of a jellyfish (Turritopsis dohrnii), , at age is given by for . (c) Find the mean mortality, . (Setup and evaluate the improper integral for the mean mortality.) 
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 

Recall the definition of mean value, and that evaluating an improper integral requires taking a limit, where the limit is applied to a proper integral. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The mean mortality is
The rightmost integral equals
And this proper integral can be evaluated by using the substitution ,
where the last equality follows from the fact that . It follows that
Hence,
