Please solve the following Markov Chain example:

(d) (5 points): What is the variance of the sojourn time for State 1? 1. (25 total points): Here are P, P2, and P3. In answering the following questions you do not have to provide a numerical answer; it will be suicient to show an expression with all of the numbers in the right places, so that only simple arithmetic needs to be completed. 0.4 0.1 0.5 0.24 0.2 0.56 0.212 0.250 0.532 P: 0.3 0.6 0.1 , P2: 031 0.41 0.28 , P3: 0.275 0.333 0.392 0.1 0.2 0.7 0.17 0.27 0.56 0.205 0.291 0.504