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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-1/6c/c/solution

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Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 1 / 6C / c / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-03

The deterministic equation has solution

n (t) = n (0) e^{(B - D) t}

and is identical in form to the equation for the stochastic expected value. It therefore identifies only the net rate

r = B - D .

The variance equation also contains the total event rate

s = B + D

. Once

r

and

s

are inferred,

B = \frac{s + r}{2}, D = \frac{s - r}{2} .

The deterministic trajectory cannot distinguish frequent births and deaths that nearly cancel from infrequent events with the same net growth, whereas fluctuations can.

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