Consider the following stochastic system. Let Xn be the price of a certain stock (rounded to the nearest cent) at the time that the stock market closes on the n-th day starting today.   Would it be appropriate to model this system as a Discrete-time Markov Chain?

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an 15 A continuous-time Markov chain (CTMC) has three states (1, 2, 3). ed dout of The average time the process stays in states 1, 2, and 3 are 3, 11.9, and 3.5 seconds, respectively. question The steady-state probability that this CTMC is in the second state ( , ) is

A bus containing 100 gamblers arrives in Las Vegas on a Monday morning. The gamblers play only poker or blackjack, and never change games during the day. The gamblers' daily choice of game can be modeled by a Markov chain: 95% of the gamblers playing poker today will play poker tomorrow, and 80% of the gamblers playing blackjack today will play blackjack tomorrow. (a) Write down the stochastic (Markov) matrix corresponding to this Markov chain. (b) If 60 gamblers play poker on Monday, how many gamblers play blackjack on Tuesday? (c) Find the unique steady-state vector for the Markov matrix in part (a).

This is a Stochastic Process question. Each customer makes claims following a Poisson process with rate 0.44 per year.For Scheme A, there are 3 discount levels: 0%, 10% and 20%.For a customer in Scheme A, he or she will move between discount levels throughout the year at continuous times.The annual premium to be paid at the start of each year is determined by the discount level he or she is in at that point of time, irrespective of the movements between the discount levels throughout the year.If a customer in Scheme A makes a claim, he or she will immediately move to a worse discount level, if possible, or remain in the 0% level.Independently of the customer making claims, for each customer in Scheme A independently the insurance company will perform a 'bump' where the customer will move to a better discount level if possible (or remain iin 20% otherwise) every so often as a customer loyalty programme with time between bumps exponentially distributed with mean 2 years. Find the…

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Suppose a Markov Chain has transition matrix % 0 % % If the system starts in state 3, what is the probability that it goes to state 2 on the next observation, and then goes to state 4 on the following observation? (A) 24 (B) 1 (C) 4 (D) ½24 (E) % (F) %32 (G) 0 (H) %

(c) Suppose there is an epidemic in which every month a quarter of those who are well become sick and 1/8 of those who are sick recover and acquire immunity for life. i. Find the matrix that describe this Markov process ii. Find the steady state of this process. Briefly justify your answer.

In a hotel, each employee is in one of three possible job classifications, and changes that classifications (independently) according to a Markov chain with transition probabilities. What percentage of employees are in each classification?