1. [18 marks] Let W1, W2, . .. be exponentially distributed iid random variables with mean 1/1, and define In = Wit . . . + Wn (To =0). Let (Nt, t 2 0) be a stochastic process defined as No = 0 and for te Rt Nt = max {n E N : W1 + . . . + Wn u) of Rit. MATH5901/3901 only: Having computed the cdf of Rt, find the cdf of the random variable Mt := The+1 -The. What is the limiting distribution of Mt as t 1 co