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

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- Solution 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} .

For completeness, when

0 < c \leq 1

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

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