3. A spider hunts a fly moving between the positions 1 and 2 according to a...
3. A spider hunts a fly moving between the positions 1 and 2 according to a Markov Chain P= 0.3 0.7 The fly, independently of the spider, moves between 1 and 2 according to a second Markov with transition matrix 0.0.3 Chain whose transition matrix is 0.4 0.6 0.6 0.4 The hunt finishes the first time both the spider and the fly are on the same position, (a) Describe the hunt with a suitable 3 states Markov Chain; (b) Assuming...
) Draw a Markov diagram modelling the following A fly moves along a straight line in unit increments. At each time period', it moves one unit to the left with probability 0.3 ¢ to the right with probability 0.3 € stays at the same place with boobability 0.4, independently of the past history of movements. A Spideo is luoking at positions 1 & m=4, if the lands there it is captured & the process terminates. Assume that the fly starts...
An insurance company classifies its customers into three categories: 1. Good Risk 2. Acceptable Risk 3. Bad Risk Customers independently transition between categories at the end of each year according to a Markov process with the following transition matrix: P = 0.6 0.3 0.1 0.5 0.0 0.5 0.4 0.4 0.2 Find the long-run proportion of time in Good Risk, and the expected number of steps needed to return to Good Risk.
Let Xn be a Markov chain with state space {0, 1, 2}, and transition probability matrix and initial distribution π = (0.2, 0.5, 0.3). Calculate P(X1 = 2) and P(X3 = 2|X0 = 0) 0.3 0.1 0.6 p0.4 0.4 0.2 0.1 0.7 0.2
(n)," 2 0) be the two-state Markov chain on states (. i} with transition probability matrix 0.7 0.3 0.4 0.6 Find P(X(2) 0 and X(5) X() 0)
1. A Markov chain has transition matrix 2 3 1 0. 0.3 0.6 ll 2 0 0.4 0.6 l 3 I| 0.3 0.20.5 I| with initial distribution a(0.2,0.3, 0.5). Find the following (a) P(X, 31X62) (c) E(X2)
2. The Markov chain (Xn, n = 0,1, 2, ...) has state space S = {1, 2, 3, 4, 5} and transition matrix (0.2 0.8 0 0 0 0.3 0.7 0 0 0 P= 0 0.3 0.5 0.1 0.1 0.3 0 0.1 0.4 0.2 1 0 0 0 0 1 ) (a) Draw the transition diagram for this Markov chain.
1. A Markov chain {X,,n0 with state space S0,1,2 has transition probability matrix 0.1 0.3 0.6 P=10.5 0.2 0.3 0.4 0.2 0.4 If P(X0-0)-P(X0-1) evaluate P[X2< X4]. 0.4 and P 0-2) 0.2. find the distribution of X2 and
A Markov chain {Xn, n ≥ 0} with state space S = {0, 1, 2} has transition probability matrix 0.1 0.3 0.6 p = 0.5 0.2 0.3 0.4 0.2 0.4 If P(X0 = 0) = P(X0 = 1) = 0.4 and P(X0 = 2) = 0.2, find the distribution of X2 and evaluate P[X2 < X4].
Consider the Markov chain with the following transition diagram. 1 0.5 0.5 0.5 0.5 0.5 2 3 0.5 (a) Write down the transition matrix of the Markov chain (b) Compute the two step transition matrix of the Markov chain 2 if the initial state distribution for 2 marks (c) What is the state distribution T2 for t t 0 is To(0.1, 0.5, 0.4)7? [3 marks (d) What is the average time 1.1 for the chain to return to state 1?...