 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/11/d/solution

Integrating the probability density function from its lower endpoint to

x

F (x) = {0, 1 - x^{- α}, x \leq 1, x > 1.

It is continuous and strictly increasing on the support. Hence the unique median

m

satisfies

F (m) = 1/2

, or

m^{- α} = 1/2

. Therefore

m = 2^{1/ α} .

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