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? (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= Down?2=

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? (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= Down?2=

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Forecasting in Business

Forecasting is the process of predicting the future based on the past and the present data and circumstances. In other words, forecasting is the act of making a detailed analysis of future events based on the decisions made in the past as well as the present. Forecasting plays a very important role in operational management as it helps in planning and decision-making. It is not only important for the success of a business but also contributes to individual growth and success. Many business organizations or companies have failed due to the shortcomings of their forecasting.

Question

From	Running	Down
	To
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?

(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=

Down?₂=

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