Please take a look at the screenshots:

(c) [5 points]: For this part, assume that the initial state is equally likely to be any one of the three states. What is the probability that the process is in State 3 at epoch 3. You need to write an expression with all of the numbers in the right places to show us how you computed your result. {cl} [5 points): What is the variance of the sojourn time for State 1? (e) [5 points]: What is the State-1 sojourn-time probabilitymass function, and its associ- ated parameters? (State this completely and clearly)- 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 sufcient to show an expression with all of the numbers in the right places, so that only.r simple arithmetic needs to he completed. 0.4 0.1 0.5 0.24 0.2 0.56 0.212 0.256 0.532 P = 0.3 0.6 0.1 , P2 = 0.31 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