 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability-resit/9/b/ii/solution

x > 0

, so the median is the unique positive

c

satisfying

F_{X} (c) = 1/2

. Consequently

e^{- c^{2} /2} = 1/2

c = 2 lo g 2 .

There is no atom at

c

, so

P (X > c) = 1 - F_{X} (c) = 1/2

as required.

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