In the tennis scoring system, once at deuce, a player needs two consecutive points to take the game: If a player wins the next point, he has advantage. On the following point, he either wins the game or the game returns to deuce. Nadal and Federer have played each other 40 times, and Nadal leads the head to head 24-16. So, we assume that Federer has probability 0.4 of winning each point and Nadal has probability 0.6 of winning each point throughout the match. At deuce, we would like to estimate the total number of points to end the game. To do this, a discrete-time stochastic process with the following five states is considered: State 1: Federer has advantage; State 2: Deuce; State 3: Nadal has advantage; State 4: Federer wins the game, and; State 5: Nadal wins the game. Question 1 Not answered Here is the transition matrix below. state X1=1 2 3 4 5 Not graded X0=1 A 0 Flag question 2 B 0 3 0 4 0 0 D 5 0 0 E Find the probability A. Answer: Question 2 Not answered Here is the transition matrix below. state X=1 2 3 4 5 Not graded X0=1 A Flag question 2 B 0 3 4 0 0 D 5 0 0 E Find the probability B. Answer: Question 3 Not answered Not graded Here is the transition matrix below. state X=1 2 3 4 5 Xo=1 A 0 Flag question 2 B 0 3 C 4 0 0 D 5 0 0 E Find the probability C. Answer: Question 4 Not answered Not graded Here is the transition matrix below. state X=1 2 3 4 Xo=1 A 0 Flag question 2 B 0 3 4 0 0 D 5 0 0 E Find the probability D. Answer: Question 5 Not answered Here is the transition matrix below. state X=1 2 3 4 Not graded X0=1 A Flag question 2 B 3 5000 4 0 0 D 5 0 0 E Find the probability E. Answer: Question 6 Not answered Not graded Flag question At deuce (State 2), what are the expected total points to end the game? Please round your answer to 2 decimal places. Answer: Question 7 Not answered Marked out of 1 Flag question Please write the steps of how you obtain this answer. Question 8 Not answered Marked out of 1 Flag question For recurrent state i, there is an "n" such that Xn=/ (it is certain to return) given that Xo-i. Please explain briefly why the process revisited the recurrent state / infinitely often.