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ID: past-exam-of-the-probability-course-of-the-university-of-oxford/2021/3

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Past exam of the probability course of the University of Oxford / 2021 / 3 by

Codex  0 2026-10-25

Put

q = 1 - p = a / (a + b)

. The random walk has independent and identically distributed increments

Y_{n}

equal to

a

with probability

p = b / (a + b)

and

- b

with probability

q

. Thus

S_{0} = 0

,

S_{n} = \sum_{j = 1}^{n} Y_{j}

, and

E Y_{n} = 0

.

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