for this result. 7. A machine consists of two parts that fail and are repaired in-...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
for this result. 7. A machine consists of two parts that fail and are repaired in- dependently. A working part fails during any given day with probability a. A part that is not working is repaired by the next day with probability b. Let X be the number of working parts in day n. (a) Show that X is a three-state Markov chain and give its one-step transition probability matrix P. (b) Show that the steady state pmf 7 is binomial with param- eter p = b/(a+b). (c) What do you expect is the steady state pmf for a machine that consists of m parts? 3. (7 points) For each of the following ARMA prcoesses, (1) Simulate a time series with 60 observations. (2) Make a sample correlogram using the simulated data. (3) Generate and plot the theoretical autocorrelation functions up to 15 lags. (a) MA(1) with 0 = 0.6 (b) MA(1) with 0 = -0.6 01 (c) MA(2) with 0 = 0.4 and 02 = 0.2 (d) AR(1) with p = 0.4 (e) AR(1) with = -0.4 (f) AR(2) with = 0.5 and 2 = -0.9 1 (g) ARMA (1,1) with = 0.7 and 0 = 0.4 for this result. 7. A machine consists of two parts that fail and are repaired in- dependently. A working part fails during any given day with probability a. A part that is not working is repaired by the next day with probability b. Let X be the number of working parts in day n. (a) Show that X is a three-state Markov chain and give its one-step transition probability matrix P. (b) Show that the steady state pmf 7 is binomial with param- eter p = b/(a+b). (c) What do you expect is the steady state pmf for a machine that consists of m parts? 3. (7 points) For each of the following ARMA prcoesses, (1) Simulate a time series with 60 observations. (2) Make a sample correlogram using the simulated data. (3) Generate and plot the theoretical autocorrelation functions up to 15 lags. (a) MA(1) with 0 = 0.6 (b) MA(1) with 0 = -0.6 01 (c) MA(2) with 0 = 0.4 and 02 = 0.2 (d) AR(1) with p = 0.4 (e) AR(1) with = -0.4 (f) AR(2) with = 0.5 and 2 = -0.9 1 (g) ARMA (1,1) with = 0.7 and 0 = 0.4
Expert Answer:
Posted Date:
Students also viewed these mathematics questions
-
The specific gravity of the dam shown in Figure P8.3.4 is 2.63, and the coefficient of friction between the dam and the foundation is 0.53. The depth of the water is 2 7.5 m when the reservoir is...
-
A 20-kg base satellite deploys three sub-satellites, each which has its own thrust capabilities, to perform research on tether propulsion. The weights of sub-satellite A, B, and C are 4 kg, 6 kg, and...
-
National paper Company must purchase a new machine for producing cardboard boxes. The company must choose between two machines. The machines produce boxes of equal quality, so the company will choose...
-
Mr. and Mrs. Coleman are going to establish a manufacturing business. They anticipate that the business will be profitable immediately due to a patent Mrs. Coleman holds. They predict that profits...
-
There is no change in enthalpy in a throttling process. State True (T) or False (F)
-
Musso Company is considering the addition of a new product to its cosmetics line. The company has three distinctly different options: a skin cream, a bath oil, or a hair coloring gel. Relevant...
-
Zeigler Manufacturing Company purchased a robot for $720,000 at the beginning of year 1. The robot has an estimated useful life of four years and an estimated residual value of $60,000. The robot,...
-
Minor impurities of group 13 or group 15 elements are introduced in order to improve the conducting ability of the semiconductor silicon. Using a band diagram, explain how each of these types of...
-
Determine the difference in semi-monthly payments between mortgage rates of 7% and 7.75% on a mortgage of $203,100.00 amortized over 20 years and payable on a semi-monthly basis.
-
How are use cases used throughout the entire system development life cycle?
-
What is an entity? What are entity instances?
-
Why is it necessary to create an implementationdependent model of a system?
-
Why is it important to create an implementationindependent model of a system?
-
What is the objective of constructing the requirements use-case model, and what steps are to be followed?
-
Revenue & Sales Corporation and Software, Inc., enter into a contract for the design of custom software for which Revenue & Sales agrees to pay $64,500. Software transfers the right to...
-
A liquid flows upward through a valve situated in a vertical pipe. Calculate the differential pressure (kPa) between points A and B. The mean velocity of the flow is 4.1 m/s. The specific gravity of...
-
If independence is essentially an attitude of mind, why is it necessary to have the auditors behaviour regulated by so many detailed rules?
-
Whinge and Grovel is a small firm of Chartered Accountants, which employs approximately fifty professional staff and provides a range of management consultancy services as well as traditional audit...
-
Considerable amounts of time and effort have been devoted to the development of a conceptual framework for accounting, so far without success. To what extent would the auditors independence be...
Study smarter with the SolutionInn App