I need help to understand the way of think this problem: "Consider a Poisson process with rate λ=4, and let N(t) be the number of arrivals during the time interval [0,t]. Suppose that you have recorded this process in a movie and that you play this movie at twice the speed. Find the new rate."
I was thinking about let M(t) be the number of arrivals in the sped-up movie. So in real time, you have watched the entire speed up movie in just t/2 and M(t)=N(t/2) => the new rate is the half of the original rate (new rate=2). Is that ok?