A hummingbird feeder has four ports where birds may feed. Birds arrive at the feeder at a rate of two per minute. If all of the ports are occupied, an arriving hummingbird will leave. Otherwise, it will begin feeding at an available port and eat for a time that has an exponential distribution with a mean of 20 seconds. Consider this as a Continuous Time Markov Chain (CTMC) process Where the state is the number of occupied ports. a) Draw the transition diagram. ( (b) Give the transition rate matrix. (c) If three ports are occupied, what is the expected time until this changes