An electric generator can be running at one of three speeds at any time: high, low, or off. It cannot change directly from high to off, nor from off to high. When it is on low, the probability is \(2 / 3\) that it will next go to high, and consequently \(1 / 3\) that it will shut off when the next change of state comes. The amount of time that the generator stays in each of the three states \(\mathrm{H}, \mathrm{L}\), and \(\mathrm{O}\) is exponentially distributed, with rates \(\lambda_{H}, \lambda_{L}\), and \(\lambda_{O}\), respectively. Model the speed as a birth-death process, and find the limiting probabilities for each state.