Please construct a counting process N, whose r.v. N(t) are distributed as Poisson(λt) but the process N itself is not a Poisson process.
This is an assignment in our Stochastic Process class. So I suppose this counting process N should meet all but one of a Poisson's process conditions. 1) N(0)=0 2) independent increments 3) At any given time t N(t) ~ Poiss( λt). So making the increments dependent should probably be the way to go. However, I've no idea how that could be done.