Hints: Centering of an inhomogeneous Poisson process

Here you need to apply the properties of the inhomogeneous Poisson process described in the problem text. Since the number of events in disjoint intervals are independent, it is useful to rewrite \(N(t) = N(t) - N(s) + N(s)\). The same goes for (b), but keep in mind that the calculations here can get a bit tedious. Note that (b) is very similar to Problem: Compensator of the Poisson process.

Solution: To get a detailed solution of the problem, see the link at the bottom of this page.