15C. Use the transition diagram to express the stochastic matrix corresponding to the states and transitions represented in this system. 0.8 A 0.2 0.3 B 0.7

Determine if the given stochastic matrix is regular. If it is regular input the smallest exponent which shows the matrix to be regular, otherwise input 0. 0.04 A = 0 0.96

Find the steady-state vector associated with the given transition matrix. (Give exact answers. Do not round.) 0.3 0.7 0.4 0.6

M * 00 T For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.13 probability of failure. Complete parts (a) through (c) below. ..... (a) Would it be unusual to observe one component fail? Two components? be unusual to observe one component fail, since the probability that one component fails, than 0.05. It V be unusual to observe two components fail, since the probability that two components fail, than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999? (Type a whole number.) O Time Remaining: 03:45:08 Next DEC 15 MacBook Air DD F7 F2 F3 F8 & 2# $ 6 R. K H. C. B. N