= Solution
{c}
A rate-two <Poisson process> starts at $N_0=0$, has independent increments and stationary increments, and has $N_{t+h}-N_t\sim\operatorname{Poisson}(2h)$ for $h\geq0$ when time is measured in minutes. Equivalently it is a counting process with independent stationary increments satisfying, uniformly in the start time,
$$
\mathbb P(\Delta N=1)=2h+o(h),\qquad \mathbb P(\Delta N\geq2)=o(h)
$$
as $h\downarrow0$. Thus an average rate alone is insufficient; the independence and increment assumptions are part of the model.
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