Question: Consider a system that alternates between the two states 0 (OFF) and 1 (ON) and that is checked at discrete time points. If the system

Consider a system that alternates between the two states 0 (OFF) and 1 (ON) and that is checked at discrete time points. If the system is OFF at one time point, the probability that it has switched to ON at the next time point is , and if it is ON, the probability that it switches to OFF is .

(a) Since the Markov property is satisfied, the system can be modeled by a Markov chain. Draw the transition graph and write down the transition matrix of the Markov chain.

(b) Suppose that = 3/4 and = 1/2 . If the system starts being OFF at time = 0, what is the probability that it is ON at time = 3?

(c) Find the stationary distribution for the Markov chain in terms of and . What do you conclude about the proportion that the system stays at OFF and ON in a long time period?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

6. Consider an electronic device that is either on-standby or in-use. The on-standby periods are exponentially distributed with mean of 15 minutes, and the in-use periods are exponential with mean of...

Here is the problem: A certain type component has two states: 0 = OFF and 1= OPERATING. In state 0, the process remains there an exponential amount of time with rate a, and then moves to state 1. The...

2.2. A certain type component has two states: 0 = OFF and 1 = OPERATING. In state 0, the process remains there a random length of time, which is exponentially distributed with parameter a, and then...

In C++, The goal of this project is to design and develop C++ code and algorithms to simulate a queue in a bank, serviced by several tellers. A second goal is to effectively employ object-oriented...

5.1. A certain type component has two states: 0 = OFF and 1 = OPERATING. In state 0, the process remains there a random length of time, which is exponentially distributed with parameter a, and then...

In the book Electrochemical Engineering I by Ivo Rousar ISBN 0-444-99562-5 an effective binary diffusion coefficient is established for a three-species system. Enclosed are the two pages 33 and 34...

6.1. A certain type component has two states: 0 = OFF and 1 = OPERATING. In state 0, the process remains there a random length of time, which is exponentially distributed with parameter a, and then...

Can you give me a detailed answer as the already existing answer in Chegg is wrong. The final answer is given below. Please provide a detailed explanation. 4. A certain type component has two states:...

6.2. A certain type component has two states: 0 = OFF and 1 = OPERATING. In state 0, the process remains there a random length of time, which is exponentially distributed with parameter a, and then...

CMPE 107 Spring 2016 Take-Home Exam MUST BE SUBMITTED IN HARD COPY BY JUNE 7 NO LATER THAN 4PM [in JJ's office or with Ali in E2 315] Grading system: presentation = 25%, content = 75% Last Name:...

An automotive warehouse stocks a variety of parts that are sold at neighborhood stores. One particular part, a popular brand of oil filter, is purchased by the warehouse for $1.50 each. It is...

Harmon's sells an average of 40 tubes of chapstick weekly. the normal price paid by Harmons is $1 per tube. it costs Harmon $25 to place an order, and Harmon's annual holding cost rate is 20%. answer...

The Indian financial system consists of which of the following major components? Question 1 7 Answer a . a ) Financial Institutions b . b ) Financial Markets c . d ) All of the above d . c )...

A project has annual cash flows of $4,500 for the next 10 years and then $9,000 each year for the following 10 years. The IRR of this 20-year project is 10.81%. If the firm's WACC is 10%, what is the...

1. Organize and support your main points

3. Move smoothly from point to point

5. Develop a strong introduction, a crucial part of all speeches