Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 2 / 11F / b / i

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- Solution i

Solution

T_{k}

the visited vertices form a contiguous arc and the walk is at an endpoint. Exiting an interval of

k

visited vertices, starting one step from an absorbing endpoint, has mean

k

. Therefore

E (T_{k + 1} - T_{k}) = k

and

E T_{n} = \sum_{k = 1}^{n - 1} k = n (n - 1) /2

.

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