 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/9/c/ii/solution

y > 0

f_{Y} (y) = 2 Φ^{'} (2 y) \frac{1}{2 y} = \frac{2}{2 π 2 y} e^{- y} = \frac{e ^{- y}}{π y} .

f_{Y} (y) = ⎩ ⎨ ⎧ \frac{e ^{- y}}{π y}, 0, y > 0, y \leq 0.

The value assigned at zero is immaterial. The probability density function is unbounded near zero, but

F_{Y} (0) = 0

1/2

and rate

1

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