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.

Answer rating: 100% (QA)

a In a Markov chain the transition probability to next step depends on the current state That is the ... View the full answer