What a basketball player makes a shot he tries a harder shot the next time and

# What a basketball player makes a shot he tries a

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7. (20 points) What a basketball player makes a shot, he tries a harder shot the next time andhits with probability 0.4. When he misses he is more conservative and hits with probability0.7. That is the the transition matrix isHMH0.40.6M0.70.3(a) He started the game by missing his first shot. What is the probability he hits his thirdshot? (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 Treesaccording to the Markov chain.GBTG1/21/20B1/63/41/12T1/605/6Find the stationary distribution. I think you will it easy to solve the equations by hand, butif you may use your calculator instead. If you do then please write out the matrix you aretaking the inverse of and not just the answer. 2
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