Ursula, an electrical engineer in a quality control department, checks silicon controlled

rectiers (SCRs) for manufacturing defects. She has noticed that when a defective SCR turned

up on the assembly line, there was a 0.07 probability that the next unit would also be defective.

If, however, an SCR passed inspection, then there was just a 0.004 likelihood that the next unit

would fail inspection.

a) Assuming that Ursula has just found a defective SCR, nd i) the initial probability vector ii) the

transition matrix iii) the probability that the next two SCRs will both fail inspection

b) Is this Markov chain regular? Explain why or why not.

c) What does your answer to part b) imply about the long-term probability of an SCR failing

inspection? Quantify your answer.