# 1. A manufacturer has a machine that, when operational at the beginning of a day, has a probability.

1. A manufacturer has a medium that, when operational at the rise of a day, has a chance of 0.1 of breach down someseason during the day. When this happens, the restore is done the present day and completed at the end of that day. (a) Formulate the evolution of the foundation of the medium as a Markov fetter by substantiateing three possible says at the end of each day, and then constructing the (one-step) transition matrix. (b) Use the approach described in Sec. 16.6 to ascertain the ij (the expected first passage season from say i to say j) for all i and j. Use these effects to substantiate the expected compute of unmeasured days that the medium gain stop operational anteriorly the present breakdown after a restore is completed. (c) Now conceive that the medium already has bybygone 20 unmeasured days externally a breakdown since the developed restore was completed. How does the expected compute of unmeasured days hereafter that the medium gain stop operational anteriorly the present breakdown parallel after a while the corresponding effect from segregate (b) when the restore had just been completed? Explain.