Decision Sciences, please answer and/or correct all questions, thank you! The co

Question

Decision Sciences, please answer and/or correct all questions, thank you!

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: a. If the system is initially running, what is the probability of the system being down in the next hour of operation? If required, . The probability of the system is b. What are the steady-state probabilities of the system being in the running state and in the down state? If required, round your answers to two decimal places. pi_1 = pi_2 =

Explanation / Answer

Ans(a):

Probability of system being down in next hour of operation = 0.10

---------------

Ans(b):

x=.9x+.3y, y=.1x+.7y
Let pi_1=P(System Running)=x
and pi_2=P(System Down)=y
then using given table we get equations:
x = .9x + 0.3y
or 0.1x-0.3y=0-----(i)

y = 0.1x + 0.7y
or -0.1x+0.3y
or 0.1x-0.3y----(ii)
we see that (i) and (ii) both are same equations so system is dependent so we can rewrite
y=0.1/0.3x or y=1/3x
we know that sum of probabilities =1
then x+y=1
x+1/3x=1
4/3x=1
x=3/4=0.75
plug into y=1/3x=1/3(0.75)=0.25
Hence the steady state distribution is given by:
pi_1=x=0.75
pi_2=y=0.25

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.