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5. Consider a system which can be in three states S = {0, 1, 2}. In state 0, the system is fully operational, in state 1 the system operates in a degraded mode, and in state 2 the system is completely failed. There is no repair, that is, when the system fails it cannot be repaired/restored into operation. The transition probability matrix of the DTMC is given by: P = [0.7 0.3 0.0 0 0.6 0.4 0 0 1] a) Draw the state transition diagram. b) Assume that the system starts in the fully operational state, nd the expected number of times the system stays in the llly operational and degraded states before a complete failure. 0) Suppose the system provider earns a prot of $10,000 when the system is fully operating and $6000 when the system is in a degraded mode per visit, what is the total prot earned by the provider before the system fails