Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
(Proof of Theorem 4.2.11) (a) Show that an ergodic Markov chain with M states must contain a cycle with τ <>M states. Hint: Use ergodicity to show that the smallest cycle cannot contain M states.
(b) Let .e be a fixed state on this cycle of length τ . Let T (m) be the set of states accessible from .e in m steps. Show that for each m ≥ 1, T (m) ⊆ T (m + τ ). Hint: For any given state j ∈ T (m), show how to construct a walk of m + τ steps from .e to j from the assumed walk of m steps.
(c) Define T (0) to be the singleton set {.e} and show that T (0) ⊆ T (τ ) ⊆ T (2τ ) ⊆ ··· ⊆ T (nτ ) ⊆ ··· .
(d) Show that if one of the inclusions above is satisfied with equality, then all subsequent inclusions are satisfied with equality. Show from this that at most the first M - 1 inclusions can be satisfied with strict inequality and that T (nτ ) = T ((M - 1)τ ) for all n ≥ M - 1.
(e) Show that all states are included in T ((M - 1)τ ).
(f) Show that P(M-1)2+1 > 0 for all i, j.
Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.
Using the following project information: Calculate the probability that the project will be completed in 38 weeks.
You have been asked to ship a package from Pennsylvania to California. You need to get it there in 2 days, heads will roll if it is late.You call 2 carriers, and ask them what their average transit time is to California.
For a customer that goes through both systems, show why the time in each system is independent of that in the other; find the distribution of the combined system time for such a customer.
What is the probability that two throws will be required to win the doll and what is the probability that more than 3 throws will be required to win the doll
Microhard has issued a bond with the following characteristics: Calculate the price of this bond if the YTM is:
Will the human subjects be informed of the nature of their involvement in the collection of data and of features of the research that reasonably might be expected to influence willingness to participate?
What is the p-value of the regression and can you reject the null hypothesis that there is no relationship between the variables at the 99% confidence level?
Given the following linear revenue and cost function for a business firm, Calculate the break - even quantity, total revenue, total cost and total profit at break - even level of production.
A bond that has a $1,000 par value (face value) and a contract or coupon interest rate of 11 percent. A new issue would have a floatation cost of 5 percent of the $1,125 market value.
What are the four components of time series plots? What programs or calculators can perform basic statistical calculations? What programs or calculators can perform multiple statistical calculations involving a large data set and multiple variables?
i already formulate the problem but i need to solve the last question how to stabilize the two ships- proportionality?
Find the probability at least one of the children will still be awake if Santa Claus arrives at midnioht - What is the probability Jack is still awake?
Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!
whatsapp: +1-415-670-9521
Phone: +1-415-670-9521
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd