What a basketball player makes a shot he tries a

7. (20 points) What a basketball player makes a shot, he tries a harder shot the next time and
hits with probability 0.4. When he misses he is more conservative and hits with probability
0.7. That is the the transition matrix is
H M
H 0 . 4 0 . 6
M 0 . 7 0 . 3
(a) He started the game by missing his first shot. What is the probability he hits his third
shot? (b) In the long run what fraction of his shots does he hit.
8. (15 points) From year to year land in a forest switches between Grass, Bushes and Trees
according to the Markov chain.
G B T
G 1 / 2 1 / 2 0
B 1 / 6 3 / 4 1 / 12
T 1 / 6 0 5 / 6
Find the stationary distribution. I think you will it easy to solve the equations by hand, but
if you may use your calculator instead. If you do then please write out the matrix you are
taking the inverse of and not just the answer.
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