 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-3/27j/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For independent identically distributed nonnegative random variables

ξ_{1}, ξ_{2}, \dots

, define the renewal epochs

S_{0} = 0, S_{n} = \sum_{i = 1}^{n} ξ_{i} .

The associated renewal process is

N (t) = max {n : S_{n} \leq t},

the number of renewals by time

t

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