PLEASE HELP ME GET THE ANSWER FOR PART B AND IT HAS TO BE FRACTION/INTEGER/ OR EXACT DECIMAL AND THE ASWER I GOT 0.66 FOR FIRST AND 0.99 FOR SECOND AND BOTHER WERE WRONG.   The computer center at Rockbottom University has been experiencing computer downtime. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
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PLEASE HELP ME GET THE ANSWER FOR PART B AND IT HAS TO BE FRACTION/INTEGER/ OR EXACT DECIMAL AND THE ASWER I GOT 0.66 FOR FIRST AND 0.99 FOR SECOND AND BOTHER WERE WRONG.
 
The computer center at Rockbottom University has been experiencing computer downtime. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities.
  To
From Running Down
Running 0.90 0.10
Down 0.20 0.80
(a)
If the system is initially running, what is the probability of the system being down in the next hour of operation?
ANSWER FOR PART A IS 0.10
(b)
What are the steady-state probabilities of the system being in the running state and in the down state? (Enter your probabilities as fractions.)
Running?1=  Your answer must be a fraction, integer, or exact decimal. .66 IS WRONG
Down?2=  Your answer must be a fraction, integer, or exact decimal. .99 IS WRONG
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