Let the independent exponential interarrival times in Example 2-1 be not identically distributed.
Give an heuristic argument on whether the counting process Nt still have independent increments. Compare it with the case of identically distributed interarrival times. (Advice: Assume, for example, that the expected value of the kth interarrival time equals k, and take into account that at any time you know how many arrivals have already occurred. Does this information matter for understanding how long we will wait for the next arrival? Say, for Δ₁ = [0,1] and Δ₂ = (1,2], compare P(N_Δ2 = 0|N_Δ1 = 1) and P(N_Δ2 = 0|N_Δ1 = 1000). )