 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/discrete-mathematics-continuous-mathematics-and-probability/9/a/iii/solution

For

c > 1

, the expected value is the convergent improper integral

E X = \int_{1}^{\infty} x \frac{c}{x ^{c + 1}} d x = c \int_{1}^{\infty} x^{- c} d x = \frac{c}{c - 1} .

0 < c \leq 1

the same positive integral diverges and the expected value is infinite.

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