Consider a counting process N_t for which interarrival times are independent and uniform on [0,1]. Show that in this case

(a) Increments of the process are dependent;

(b) The process is not Markov. Does your answer to the second question answer the first? Give an answer to the first question proceeding directly from the distribution of increments. Give a common-sense explanation of your results. (Advice: For intervals Δ₁ = [0,0.5] and Δ₂ = (0.5,1], consider P(N_Δ2 = 0|N_Δ1 =0) and P(N_Δ2 = 0|N_Δ1 = 1). Also, compare P(N₂ = 2|N_1.5 = 2,N₁ = 2) and P(N₂ = 2|N_1.5 = 2).)