Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 1 / e

Table of contents
- i e
  - Solution i
- ii e
  - Solution ii

i

Solution

The two event clocks have independent exponential distributions with rates

μ

and

γ

. The competing exponential clocks identity gives

P_{I} (D before R) = \frac{μ}{μ + γ} .

ii

Solution

The minimum of the recovery and death clocks has an exponential distribution with rate

μ + γ

. Its expected value is therefore

E_{I} [T_{{R, D}}] = \frac{1}{μ + γ} .

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