The state of a component in a machine is described by a discrete-time Markov chain with state space S {1,2,3} and 1-step transition matrix P = 0 = The machine contains 25 of these components which all behave, independently of each other, according to the Markov chain described above. Now assume that whenever a component reaches state 3, it is instantaneously replaced by a new component which starts with probability 1/2 in state 1 and with probability 1/2 in state 2. A) Explain how the state of an arbitrary component in the machine can alternatively be described by a discrete-time Markov chain with only 22 states and use this alternative description to show that in the long-run on average 1010 components in the machine are in state 11 and 1515 components in the machine are in state 22. B) What is the expected number of components that will be replaced per time period?