Question

There is a square mat and a cat sitting on one of the corners. The cat will jump between the four corners of the mat. Every time the cat jumps, it has a probability of 1/4 of jumping to each of the two adjacent corners, probability 1/6 of jumping to the corner diagonally opposite, and probability 1/3 of jumping straight up and down and staying on the same corner.

Write the transition matrix A for this Markov chain.

Answer 1

To write the transition matrix A for this Markov chain representing the cat's movement on a square mat, label the corners as A, B, C, and D. The transition matrix is A = [[1/4, 1/4, 1/6, 1/3], [1/4, 1/4, 1/6, 1/3], [1/4, 1/4, 1/6, 1/3], [1/4, 1/4, 1/6, 1/3]].

Step-by-step explanation:

To write the transition matrix A for this Markov chain, we need to determine the transition probabilities for each state and its possible transitions to other states.

In this case, the Markov chain represents the cat's movement between the four corners of the square mat.

Let's label the corners of the mat as A, B, C, and D, clockwise starting from the top-left corner.

Based on the given probabilities, we can determine the transition matrix A as follows:

A = [[1/4, 1/4, 1/6, 1/3], [1/4, 1/4, 1/6, 1/3], [1/4, 1/4, 1/6, 1/3], [1/4, 1/4, 1/6, 1/3]]