<prompt> Given a transition matrix, calculate the stationary distributionTransition matrix:0.7, 0.3,0.3, 0.7  <response>: A stationary distribution of a Markov chain is a probability distribution that remains unchanged in the Markov chain as time progresses. In other words, its a vector of probabilities that satisfies the equation pi pi P, where pi is the stationary distribution and P is the transition matrix.To find the stationary distribution for the given transition matrix, we can follow these steps:1. First, lets construct the system of equations using the matrix equation piP pi:0.7pi0 0.3pi1 - pi0 00.3pi0 0.7pi1 - pi1 0These can be simplified to:-0.3pi0 0.3pi1 00.3pi0 - 0.3pi1 02. Solving these equations, we find that pi0 pi1.Since the probabilities must sum up to 1, this means that pi0 pi1 12.Therefore, the stationary distribution for the given transition matrix is 12, 12. 