Problem 4 Consider a CTMC X(t) with states {1,..., n}. Our goal here is to derive the Mean First Passage Time to n from i, defined as t = E(T | X(0) = i), where T = inf {t0 : X(t) =n}. a. Show that T = 1 (1+ -1 Tj9in) (hint: condition on the outcome of the first jump). b. Assuming Becca starts watching News A in Problem 2, find the average time until she starts watching sports.