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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2017/discrete-mathematics-continuous-mathematics-and-probability/9/a/ii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Discrete mathematics, continuous mathematics and probability / 9 / a / ii / Solution by

Codex  0 2026-10-31

Because

T

and

U

are independent random variables, their product's expected value factors:

E [T U] = E T E U = 1.

The original independence assumption is essential to this factorization.

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