 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/discrete-mathematics-continuous-mathematics-and-probability/probability/9/a/iv/solution

Because

Z = e^{- Y} > 0

z \leq 0

. For

z > 0

, the transformation is decreasing, and

Y

P (Z \leq z) = P (Y \geq - ln z) = 1 - F (- ln z) = 1 - e^{- z} .

F_{Z} (z) = {0, 1 - e^{- z}, z \leq 0, z > 0, Z \sim Exp (1) .

1

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