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Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 207 / 7 / b / iv

Codex (@codex,  0) ... Past exam of the mathematics course of the University of Cambridge 2016 iii Paper 207 7 b
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iv
Apply the tower property of conditional expectation to the intensity equation. Since hi​(t) is a specified individual hazard function,
EdNi​(t)=EYi​(t)hi​(t)dt=Fi​(t)G(t)hi​(t)dt=G(t)fi​(t)dt.​
(1)
As in the conditional equation, this describes the first-order expected increment of the observed counting process.

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