A Markov chain ( left X 0 , X 1 , ldots ight ) has state space ( mathbf Z 0,1,2 ) and transition matrix mathbf P left( begin array ccc 0 0 4 0 6 0 8 0 0 2 0 5 0 5 0 end array ight) (1) Given the initial distribution (P left(X 0 0 ight) P left(X 0 1 ight) 0 4 ) and (P left(X 0 2 ight) 0 2 ), determi...

A Markov chain (left{X_{0}, X_{1}, ldots ight}) has state space (mathbf{Z}={0,1,2}) and transition matrix [mathbf{P}=left(begin{array}{ccc} 0 &

Question:

A Markov chain $\left\{X_{0}, X_{1}, \ldots\right\}$ has state space $\mathbf{Z}=\{0,1,2\}$ and transition matrix

\[\mathbf{P}=\left(\begin{array}{ccc} 0 & 0.4 & 0.6 \\ 0.8 & 0 & 0.2 \\ 0.5 & 0.5 & 0 \end{array}\right)\]

(1) Given the initial distribution $P\left(X_{0}=0\right)=P\left(X_{0}=1\right)=0.4$ and $P\left(X_{0}=2\right)=0.2$, determine $P\left(X_{3}=2\right)$.

(2) Draw the corresponding transition graph.

(3) Determine the stationary distribution.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Probability And Stochastic Processes

ISBN: 9780367658496

2nd Edition

Authors: Frank Beichelt

See More Books

Question Posted: Apr 26, 2024 04:01 PM

See More Questions

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
Write a SET client SpellChecker that takes as a commandline argument the name of a file containing a dictionary of words, and then reads strings from standard input and prints any string that is not...
Calculate the expected return: State of Economy ____Probability of State of Economy _____Portfolio Return If State Occurs Recession .................................
ABC, wholesale, customer profitability Ramirez Wholesalers operates at capacity and sells furniture items to four department-store chains (customers). Mr. Ramirez commented, "We apply ABC to...
The shear creep compliance, $S_{66}(t)$ for a unidirectional viscoelastic composite is given by $S_{66}(t)=\gamma_{12}(t) / \tau_{12}$, where $\gamma_{12}(t)$ is the time-dependent shear creep...
Assume currently the price of a stock is $20 and a bank sold 100,000 call options on this stock with a strike price of $15. The bank wants to use delta hedging to protect itself. The price changes...
Molly Ellen, bookkeeper for Keystone Company, forgot to send in the payroll taxes due on April 15. She sent the payment November 8. The IRS sent her a penalty charge of 9.60% simple interest on the...
Let $\left\{Y_{0}, Y_{1}, \ldots ight\}$ be a sequence of independent, identically distributed binary random variables with $P\left(Y_{i}=0 ight)=P\left(Y_{i}=1 ight)=1 / 2 ; i=0,1, \ldots$....
A Markov chain $\left\{X_{0}, X_{1}, \ldots ight\}$ has state space $\mathbf{Z}=\{0,1,2\}$ and transition matrix \[\mathbf{P}=\left(\begin{array}{ccc} 0.2 & 0.3 & 0.5 \\ 0.8 & 0.2 & 0 \\ 0.6 & 0...
Zak Corp. purchased depreciable assets costing $600,000 on January 2, 2023. For tax purposes, the company uses CCA in a class that has a 40% rate. Assume these assets are considered eligible...
How much will be accumulated at the end of 25 years if an investor sets aside $450 at the end of each month and earns an average return of 9.5%?
Calculate the amount of loss because of the NPT for each rig in 2018. NPT2018 NPTHours NPT Percentage CostImpact(USD) Rig1 648.25 8.04% 748,843.80 Rig2 734.50 9.21% 825,000.00 Rig3 658.50 8.06%...
Why do firefighters need to know what to expect on a call? Discuss.
Borrowed $83,500 from a bank, signing a short-term note payable. Provided $106,200 in service to customers, with $100,000 on account and the rest received in cash. Purchased equipment for $189,000 in...
How to calculate coupon bond's Yields to Maturity? Table 1 Yields to Maturity on a 10%-coupon-Rate Bond Maturing in Ten Years (Face Value = $1,000) Price of Bond ($) Yield to Maturity (%) 1,200 7.13...
Two pans of a balance are 50.0 cm apart. The fulcrum of the balance has been shifted 1.00 cm away from the center by a dishonest shopkeeper. By what percentage is the true weight of the goods being...
Graph one period of each function. y = 4 cos x
Company PQR is considering issuing new equity at a cost of 12%. The company's investment bank charges a 5% underwriting fee on the gross proceeds. Calculate the flotation cost as a percentage of the...
Income Statement Sales $250,000 Costs $120,000 Other Expenses $20,000 Depreciation $15,000 EBIT $95,000 Interest $29,000 Taxable Income $66,000 Taxes $23,100 Net Income $42,900 Dividends $12,870...
Sales Costs Other Expenses Depreciation EBIT Interest Taxable Income Taxes Net Income Dividends Retained Earnings $250,000 $120,000 $20,000 $15,000 $95.000 $29,000 S66,000 S23,100 $42.900 $12.870...

A Markov chain (left{X_{0}, X_{1}, ldots ight}) has state space (mathbf{Z}={0,1,2}) and transition matrix [mathbf{P}=left(begin{array}{ccc} 0 &

Question:

Step by Step Answer:

Da...View the full answer

Applied Probability And Stochastic Processes

Students also viewed these Business questions