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3. Ally bases her price to act in a movie on the success of her last two movies. Movies may be a blockbuster (B),

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3. Ally bases her price to act in a movie on the success of her last two movies. Movies may be a blockbuster (B), average (A) or a dud (D). Below is her rate table: Last Two Movies Both Blockbusters At Least One Blockbuster Two Average Otherwise Rate $4 million $3 million $2 million $1 million As it turns out, the success of her next film only depends on the success of the most recent films. After a blockbuster, her next film is a blockbuster 40% of the time, an average film 40% of the time and a dud 20% of the time. After an average film, her next film is a blockbuster 30% of the time, an average film 50% of the time and a dud 20% of the time. After a dud, her next film is a blockbuster 20% of the time, an average film 50% of the time and a dud 30% of the time. a. Note that Ally's rate requires that one know the outcome of the two most recent films. How would you define the state for this system? What are the possible states (hint: there should be more that 3)? b. Develop the transition probably matrix for this system (it may be helpful to draw the state transition diagram first). c. What are the steady state values for each of your states? d. What is Ally's average rate per film?

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