answer all questions with explanation

(25 points, 5 each). 3 students Ellen (E), James (J) and Nancy (N) independently each depart Columbia University at the same time to travel to Utopia. Assume that the length of time it will take each to get there E, J, N are independent exponential random variables at rates 1/10, 1/20, 1/5 (time is in days), hence means 10, 20, 5 days respectively. (a) What is the probability that James arrives to Utopia before Nancy? (b) Given that James arrives to Utopia before Nancy, what is his expected length of time? (c) What is the probability that James is the rst one (out of all 3) to arrive at Utopia? (d) Let X = the time until the rst of them (whomever it is of the 3) arrives to Utopia. Compute E(X) (e) 4 days after they departed, none of them has yet arrived to Utopia. Compute E(X) from (d) now