A golfer practices chipping and putting for hours on end. He uses 3 clubs topractice: a putter, a sand wedge, and a pitching wedge. The amount of time that he useseach club is exponentially distributed. The golfer uses his putter for an average of 15 minutes,and he then switches to the sand wedge or to the pitching wedge with equal probability. If1the golfer is using the sand wedge, he will always switch to a pitching wedge after an averageof 30 minutes. The golfer uses a pitching wedge for an average of 10 minutes, then switches to the putter with probability 0.75 or to the sand wedge with probability 0.25.

(a) Draw the CTMC rate diagram, clearly label your states and transition rates(qij 's)

(b) Find the transition rates out of the states (vi's) and transition probabilities(Pij 's).

(c) Find the limiting probabilities (make sure to write out the balance equations).(d) (5 points) In the long run, what is the probability that the golfer is not using the putter?

(e) The golfer is trying to learn how not to hit the ball too hard. If he hits theball too hard twenty percent of the times he hits it with a putter, 10 percent of the timeshe hits it with a sand wedge and 40 percent of the times he hits it with the pitchingwedge, what proportion of the time does he hit the ball too hard?