Pr{A = k} otherwise andom sequence {X;}, as: А, li>1: if X; = 1 Xi+1 if X; = 2 Xi+1 if X; = 3 Xi+1 }, Markov? e the random sequence {Y;} according to: 1 if X; = 1 2 otherwise Y; = that {Y;}, is not Markov.
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- 4. Suppose X0, X1, X2,... are iid Binomial (2, 5). If we view this sequence as a Markov chain with S = {0,1,2}, what is its PTM?3.2: Markov Chains are Proper Probabilistic Models Show that the sum of the probabilities over all possible sequences of any length is 1. This proves that the Markov chain describes a proper probability distribution over the whole space of sequences.A study of armed robbers yielded the approximate transition probability matrix shown below. The matrix gives the probability that a robber currents free, on probation, or in jail would, over a period of a year, make a transition to one of the states. То From Free Probation Jail Free 0.7 0.2 0.1 Probation 0.3 0.5 0.2 Jail 0.0 0.1 0.9 Assuming that transitions are recorded at the end of each one-year period: i) For a robber who is now free, what is the expected number of years before going to jail? ii) What proportion of time can a robber expect to spend in jail? [Note: You may consider maximum four transitions as equivalent to that of steady state if you like.]
- 6We will use Markov chain to model weather XYZ city. According to the city’s meteorologist, every day in XYZ is either sunny, cloudy or rainy. The meteorologist have informed us that the city never has two consecutive sunny days. If it is sunny one day, then it is equally likely to be either cloudy or rainy the next day. If it is rainy or cloudy one day, then there is one chance in two that it will be the same the next possibilities. In the long run, what proportion of days are cloudy, sunny and rainy? Show the transition matrix.5. Explain what is meant by BLUE estimates and the Gauss-Markov theorem. Mathematics relevant proofs will be rewarded. [:
- Which statements are true? Select one or more: a. Markov’s inequality is only useful if I am interested in that X is larger than its expectation. b. Chebyshev’s inequality gives better bounds than Markov’s inequality. c. Markov’s inequality is easier to use. d. One can prove Chebyshev’s inequality using Markov’s inequality with (X−E(X))2.A coffee shop has two coffee machines, and only one coffee machine is in operation at any given time. A coffee machine may break down on any given day with probability 0.2 and it is impossible that both coffee machines break down on the same day. There is a repair store close to this coffee shop and it takes 2 days to fix the coffee machine completely. This repair store can only handle one broken coffee machine at a time. Define your own Markov chain and use it to compute the proportion of time in the long run that there is no coffee machine in operation in the coffee shop at the end of the day.Pls help
- prove the propertyQ3) The state transition matrix of a Markov random process is given by 1/3 1/3 1/6 1/6 5/9 0 0 4/9 2/5 1/5 1/5 1/5 0 0 3/20 17/20 [ ] Draw the state transition diagram and denote all the state transition probabilities on the same. Find P[X1 = 2] List the pairs of communicating states. Find P[X2 = 3| X1 = 2] Compute P[X2 = 2 | X0 = 1] Compute P[X3 = 3, X2 = 1, X1 = 2 | X0 = 3] (vii) Find P[X4 = 4, X3 = 3, X2 = 3, X1 = 1, X0 =2] where Xt denotes the state of the random process at time instant t. The initial probability distribution is given by X0 = [2/5 1/5 1/5 1/5].Which of the following best describes the long-run probabilities of a Markov chain {Xn: n = 0, 1, 2, ...}? O the probabilities of eventually returning to a state having previously been in that state O the fraction of time the states are repeated on the next step O the fraction of the time being in the various states in the long run O the probabilities of starting in the various states • Previous Not saved Simpfun