Reference no: EM13909170
Consider a Markov process for which the embedded Markov chain is a birth-death chain with transition probabilities Pi,i+1 = 2/5 for all i ≥ 1, Pi,i-1 = 3/5 for all i ≥ 1, P01 = 1, and Pij = 0 otherwise.
(a) Find the steady-state probabilities {πi; i ≥ 0} for the embedded chain.
(b) Assume that the transition rate out of state i, for i ≥ 0, is given by νi = 2-i. Find the transition rates {qij} between states and show that there is no probability vector solution {pi; i ≥ 0} to (7.23).
(c) Argue that the expected time between visits to any given state i is infinite. Find the expected number of transitions between visits to any given state i. Argue that, starting from any state i, an eventual return to state ioccurs with probability 1.
(d) Consider the sampled-time approximation of this process with δ = 1. Draw the graph of the resulting Markov chain and argue why it must be null recurrent.
Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.
|
Provide a safe and nurturing environment for employees
: provide a safe and nurturing environment for employees
|
|
What must the expected return on the market be
: A stock has an expected return of 8 percent, its beta is 0.85, and the risk-free rate is 3.6 percent. What must the expected return on the market be?
|
|
Discussions about the quality of the product
: Section will provide a comprehensive look at the products, product lines, and services that are offered by your company. This will include discussions about the quality of the product/service and other additions such as warranties,installation, servi..
|
|
Describe any four rights of users of information systems
: Describe any four rights of users of information systems. Explain the term virus and explain the differences between Trojan horses and worms. Support your answers with examples.
|
|
Find expected number of transition between visits to state i
: Find the expected number of transitions between visits to any given state i. Argue that, starting from any state i, an eventual return to state ioccurs with probability 1.
|
|
Definition of the set spic of pictures
: Consider an app that draws "suit" pictures. The simplest pictures one can draw are ♣ and ♠. Give the inductive definition of the set SPic of pictures
|
|
Sarbanes-oxley and corporate governance paper
: If auditing of financial statements is required for the protection of public investors, should not all PCAOB members be taken from the investment community that uses audited financial statements? Why or why not?How does the decision in this case impa..
|
|
Energy vs reaction coordinate graph
: Compare two reactions by drawing them on Energy vs. Reaction Coordinate graph. The reactions are identical, but one has been altered by the addition of a catalyst and/or enzyme. Label the ΔG and Ea for each reaction accordingly.
|
|
What are global is management challenges that face is leader
: What are some of the global IS management challenges that face IS leaders today and Why is it important for an organization to have an information security policy?
|