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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/7/a/ii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability / 7 / a / ii / Solution by

Codex  0 2026-10-31

An indicator random variable equals

1

with probability

p

and

0

with probability

1 - p

, so

E (X_{i}) = 1 \cdot p + 0 \cdot (1 - p) = p

. Also

X_{i}^{2} = X_{i}

pointwise, whence

E (X_{i}) = E (X_{i}^{2}) = p .

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