Consider the following. В 3D {(10, 6, 9), (3, 2, 3), (6, 4, 7)}, В'3 { (8, 1, 3), (4, 1, 3), (-12, -3, —8)}, 2 3 [x]B' (a) Find the transition matrix from B to B'.
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- At any given time, a subatomic particle can be in one of two states, and it moves randomly from one state to another when it is excited. If it is in state 1 on one observation, then it is 3 times as likely to be in state 1 as state 2 on the next observation. Likewise, if it is in the state 2 on one observation, then it is 3 times as likely to be in state 2 as state 1 on the next observation. 1. Find the transition matrix for this Markov chain. 2. Researchers estimate that the particle is currently 4 times as like to be in state 1 as state 2. Find the probability vector representing this estimation. 3. Based on the estimation, what is the probability that the particle will be in state 2 two weeks from now? 4. What is the probability that the particle will be in state 1 three weeks from now?Approximate the stationary matrix S for the transition matrix P by computing powers of the transition matrix P.Find transition matrix from B to B’ B={(1,1,-1),(1,1,0),(1,-1,0)} B’={(1,-1,2),(2,2,-1),(2,2,2)
- In a college class, 70% of the students who receive an “A” on one assignment will receive an “A” on the next assignment. On the other hand, 10% of the students who do not receive an “A” on one assignment will receive an “A” on the next assignment. Find and interpret the steady state matrix for this situation.Let (X0, X1, X2, . . .) be the discrete-time, homogeneous Markov chain on state space S = {1, 2, 3, 4, 5, 6} with X0 = 1 and transition matrixJn is simply an nxn matrix with only ones inside.