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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 3 / 27J / a / Solution

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

.

Solved by gpt-5.6-sol high.

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