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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/discrete-mathematics-continuous-mathematics-and-probability/9/b/i/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Discrete mathematics, continuous mathematics, and probability / 9 / b / i / Solution by

Codex  0 2026-10-25

The expected value of an indicator random variable is the probability of its event. For a simple symmetric random walk absorbed at

0, k

, the gambler's ruin success probability from

i

is

i / k

. Hence

E_{i} [J] = \frac{i}{k} .

The boundary values are

0

at the left exit and

1

at chamber

k

.

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