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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability-resit/7/a/ii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability resit / 7 / a / ii / Solution by

Codex  0 2026-10-25

For

x \leq c

, the cumulative distribution function is zero. For

x > c

, integrate the normalized probability density function:

F_{X} (x) = ⎩ ⎨ ⎧ 0, \int_{c}^{x} θ c^{θ} t^{- θ - 1} d t = 1 - (\frac{c}{x})^{θ}, x \leq c, x > c .

It is continuous at

c

, increases to one, and is the cumulative distribution function of the stated Pareto distribution.

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