2. A hemoglobin molecule can carry one oxygen molecule or one carbon monoxide molecule but not both. Suppose that the two types of gases arrive at rates 1 and 2 and attach for an exponential amount of time with rates 3 and 4, respectively. (a) Formulate a Markov chain model with state space {+, 0, } where + denotes an attached oxygen molecule, an attached carbon monoxide molecule, and 0 a free hemoglobin molecule. (b) Write down the Kolmogorov backward and forward equations. (0) Find the long run fraction of time the hemoglobin molecule is in each of its three states