MATH103 April 2017
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) (i) • Q1 (e) (ii) • Q1 (e) (iii) • Q1 (f) • Q2 (a) • Q2 (b) (i) • Q2 (b) (ii) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 • Q5 • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) • Q8 (c) • Q9 (a) • Q9 (b) • Q9 (c) • Q9 (d) • Q9 (e) •
Question 09 (c)
The probability density function (pdf ) for the mortality of a jellyfish (Turritopsis dohrnii),
, at age is given by
(c) Find the mean mortality, .
(Setup and evaluate the improper integral for the mean mortality.)
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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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The mean mortality is
The right-most 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