Except that time is *not* a Poisson process. Time is isochronous
(by definition), and isochronous processes are not Poisson. (Events
in a Poisson process are characterized by an exponential probability
distribution.)
This distinction can actually matter, as Steve McCanne and I showed
in a paper given at a Usenix in the 1990s. Unix-like systems whose
scheduler is driven from the same clock as their "random" (actually
not random at all!) sampling clock provide just what is needed to
write programs whose resource usage is systematically mismeasured.
This sort of mis-measuring can and does occur "by accident", as
well as on purpose in our "hog.c" program (which uses more than
90% of the available CPU time, even though "ps" commands show it
using under 5%).
To get accurate measurements, many modern CPUs provide a clock-cycle
counter. Using it requires a lot of careful attention to details,
all of which are, unfortunately, off-topic in comp.lang.c.