i need this question done in 10 minutes 2. (a) A Markov chain X = {X, 0} is used for a competing risk analysis based on thefollowing simple diagram with the respective transition ratesHE175E2Figure 1: Transition diagram of a simple competing risk model.where H represents a healthy state, E₁ event of interest, and E2 other type of exit.i. Write down the intensity matrix of the Markov chain.ii. Find the transition probability Phe₁(t) = P(X₁ = E₁|X0 = H) of moving from a healthystate to the event of interest.iii. Find the expected remaining lifetime of a healthy subject.=(b) From the observations of sample paths of Markov chain X {X, t≥ 0} with state spaceS = {1,2,3}, the number of transitions Nij between states i, j = S and the length of timeZ; spent in each state i = S are reported in the matrices below0 20 3010N = 40 0 5010 20 0Z =205Elements qij of the intensity matrix Q is found as the maximizer of likelihood function3 3L({ij}) = [[((ij)i=1 j#ii. Find the estimate 7i; of the intensity qij.ii. Use the given observations to find an estimate of the intensity matrix Q.

Markov Chain AnalysisPart (a)i. Intensity Matrix:The intensity matrix Q is given by:Q = | -7 7 0…

Answered: 2. (a) A Markov chain X = {X, 0} is…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.

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Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.
Mini Case Consider a portfolio consisting of N-500 assets with equal credit ratings. Assume that for every asset i E {1, ..., N} the notional is 10,000 USD, the EAD is equal to 100%, PD;=2%, LGD;=30%, i € {1,..., N} and LGDs are deterministic. Defaults are assumed to be statistically independent. Derive the expected value and standard deviation of the portfolio loss. Hint: The default indicator of asset i E {1,..., N} is Iį ~ B(1, PD;).
Let's consider a supermarket with three cash registers. The operation of the cash registers is checked daily, and if a register is found to be faulty, it is sent to the workshop for repairs. The probability of a working cash register breaking down is 1/5, and the probability of a cash register undergoing repair becoming operational is 3/5. The processes of breakdown and repair of cash registers are independent of each other. 1. (25 pts) Model this problem using a discrete time Markov chain. Present the transition probability matrix. 2. (15 pts) What is the long-run proportion of days when none of the cash registers are operational?
Please do the questions with handwritten working. I'm struggling to understand what to write
43.10. Permanent disability is modeled as a Markov chain with three states: healthy (state 0), disabled (state 1), and dead (state 2). You are given the following transition forces: 0.05 5 (1) = 0.10 r>5 (i) 4, =0.02 (iii) p,-0.02 Calculate the probability that a healthy person age x will be dead at age x +10.
The computer center at Rockbottom University has been experiencing computer downtime. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities. To From Running Down Running 0.90 0.10 Down 0.20 0.80 (a) If the system is initially running, what is the probability of the system being down in the next hour of operation? (b) What are the steady-state probabilities of the system being in the running state and in the down state? (Enter your probabilities as fractions.) Running?1= Down?2=
A major long-distance telephone company (company A) has studied the tendency of telephone users to switch from one carrier to another. The company believes that over successive six-month periods, the probability that a customer who uses A's service will switch to a competing service is 0.2 and the probability that a customer of any competing service will switch to A is 0.3. (a) Find a transition matrix for this situation. (b) If A presently controls 60% of the market, what percentage can it expect to control six months from now? (c) What percentage of the market can A expect to control in the long run? (a) Find a transition matrix for this situation. Let "Comp" stand for "a competing service." A Comp A Comp (Type integers or decimals.) (b) If A presently controls 60% of the market, what percentage can it expect to control six months from now? Company A can expect to control % of the market six months from now. (c) What percentage of the market can A expect to control in the long run?…
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Please do question 3c with full working out. I'm struggling to understand what to write
Consider a set of three assets, one risk-free and two risky. The covariance matrix [0.36 0.07] for the risky assets is given by = 0.07 The risk-free rate is 0.03 0.07 0.29 and risk aversion is A = 4. Calculate the optimal portfolio for this individual.
2. Consider the continuous-time Markov chain with the transition rate matrix -1 1 1 -2 1 2 -2 (a) Find its stationary distribution. (b) Find the transition probability matrix of the embedded chain of this continuous-time Markov chain.
The computer center at Rockbottom University has been experiencing computer downtime. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities. From Running Running 0.90 Down To 0.20 Down 0.10 0.80 (a) If the system is initially running, what is the probability of the system being down in the next hour of operation? (b) What are the steady-state probabilities of the system being in the running state and in the down state? (Enter your probabilities as fractions.) Running #1 Down #2

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