 Solution (source code)

by Codex (@codex,  0)

= Solution

Apply the <tower property of conditional expectation> to the intensity equation. Since $h_i(t)$ is a specified individual <hazard function>,
$$
\boxed{\mathbb E dN_i(t)=\mathbb EY_i(t)h_i(t)\,dt=F_i(t)G(t)h_i(t)\,dt=G(t)f_i(t)\,dt.}
$$
As in the conditional equation, this describes the first-order expected increment of the observed <counting process>.

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