Question

(20) 1.A certain stock price has been observed to follow a pattern. If the stock price goes up one day, there's a 20% chance of it rising tomorrow, a 30% chance of it falling, and a 50% chance of it remaining the same. If the stock price falls one day, there's a 35% chance of it rising tomorrow, a 50% chance of it falling, and a 15% chance of it remaining the same. Finally, if the price is stable on one day, then it has a 50-50 change of rising or falling the next day. (10) (a) Model this as a Markov chain. Classify the states of this Markov chain. That is classify the classes, identify each state and specify the period of each state. (10) (b) Compute the long run fraction of time that the stock is rising?

          (20) 1.A certain stock price has been observed to follow a pattern. If the stock price goes up one day, there's a 20% chance of it rising tomorrow, a 30% chance of it falling, and a 50% chance of it remaining the same. If the stock price falls one day, there's a 35% chance of it rising tomorrow, a 50% chance of it falling, and a 15% chance of it remaining the same. Finally, if the price is stable on one day, then it has a 50-50 change of rising or falling the next day.
(10) (a) Model this as a Markov chain. Classify the states of this Markov chain. That is classify the classes, identify each state and specify the period of each state.
(10) (b) Compute the long run fraction of time that the stock is rising?

$(20) 1.A certain stock price has been observed to follow a pattern. If the stock price goes up one day, there's a 20% chance of it rising tomorrow, a 30% chance of it falling, and a 50% chance of it remaining the same. If the stock price falls one day, there's a 35% chance of it rising tomorrow, a 50% chance of it falling, and a 15% chance of it remaining the same. Finally, if the price is stable on one day, then it has a 50-50 change of rising or falling the next day. (10) (a) Model this as a Markov chain. Classify the states of this Markov chain. That is classify the classes, identify each state and specify the period of each state. (10) (b) Compute the long run fraction of time that the stock is rising?$

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