Joe Zilch is practicing basketball by repeatedly making attempts (shots) to put the ball in the basket.
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Question:
Joe Zilch is practicing basketball by repeatedly making attempts (shots) to put the ball in the basket. We label his first shot as random variable (RV) X 1 , second shot as X 2 , ..., nth shot as X n , etc. When he takes the nth shot, he either makes a basket ( X n =1) or misses
( X n = 0 ). He finds that the result of any shot Xn depends on the outcome of his last two shots X n−2 and X n−1 as follows:
P( X n =1 | he missed both of his last two shots) = 1/2
P(X n =1 | he made one of his last two shots) = 2/3
P(X n =1 | he made both of his last two shots) = 3/4(a). Show how Joe's basketball play may be modeled using a Markov chain. How many states are needed? (Hint: Define a state as the outcome of his last two shots). Draw a labeled state transition diagram or trellis describing the process.(b). Find the transition matrix P for the process.
Related Book For
Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers
ISBN: 978-1118324561
3rd edition
Authors: Roy D. Yates, David J. Goodman
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