The following transition matrix models a random walk along the verticies of a triangle: [0.8 0.1...

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The following transition matrix models a random walk along the verticies of a triangle: [0.8 0.1 0.1] R = 0.1 0.8 0.1 0.1 0.1 0.8 (a) What is the likelihood in one step that a walker changes direction? (b) Compute the eigenvalues of R. (c) Find the matrix P that diagonalises R. (d) Suppose a large number of walkers start at the first vertex of the triangle. How many time steps until the proportion of walkers at the first vertex is no more than ½ +0.01? How long until it is no larger than ½ +0.0001? The following transition matrix models a random walk along the verticies of a triangle: [0.8 0.1 0.1] R = 0.1 0.8 0.1 0.1 0.1 0.8 (a) What is the likelihood in one step that a walker changes direction? (b) Compute the eigenvalues of R. (c) Find the matrix P that diagonalises R. (d) Suppose a large number of walkers start at the first vertex of the triangle. How many time steps until the proportion of walkers at the first vertex is no more than ½ +0.01? How long until it is no larger than ½ +0.0001?