2. Suppose that in a different city Finns opens a new studio, and this studio offers a Lifetime package. The Lifetime package means that once a family buys this package, they are permanently in this state. Market research shows that the only families that will buy the Lifetime package are ones that bought the deluxe package the year before, but only 3% of them. Research also shows that this is a tougher market than the first one. If a family did not purchase a portrait package last year, then there is a 7% chance that they will buy a regular package, and a 2% chance that they will buy a deluxe package. If a family purchased a regular package last year, then there is a 50% chance that they will not purchase a package this year, but a 12% chance that they will buy a deluxe package. If a family purchased a deluxe package last year, there is a 25% chance that they will not buy a package this year, a 32% chance that they will buy a standard package, and we already mentioned that there is a 3% chance that they will buy the Lifetime package.(b) Suppose the studio has a grand opening this year. What willthe percentages of the different packages bought in the 12th year be? Round the percents to two decimal places. Interpret your answers using complete sentence(s).

2. Suppose that in a different city "Finn's opens a new studio, and this studio offers a "Lifetime package. The Lifetime package means that once a family buys this package, they are permanently in this state. Market research shows that the only families that will buy the Lifetime package are ones that bought the deluxe package the year before, but only 3% of them. Research also shows that this is a tougher market than the first one. If a family did not purchase a portrait package last year, then there is a 7% chance that they will buy a regular package, and a 2% chance that they will buy a deluxe package. If a family purchased a regular package last year, then there is a 50% chance that they will not purchase a package this year, but a 12% chance that they will buy a deluxe package. If a family purchased a deluxe package last year, there is a 25% chance that they will not buy a package this year, a 32% chance that they will buy a standard package, and we already mentioned that there is a 3% chance that they will buy the Lifetime package. (a) Construct a matrix of transition probabilities for this scenario. (b) Suppose the studio has a grand opening this year. What will the percentages of the different packages bought in the 12th year be? Round the percents to two decimal places. Interpret your answers using complete sentence(s). (c) What is the steady state solution? Is this reasonable for this scenario? Explain using complete sentence(s). 2. Suppose that in a different city "Finn's opens a new studio, and this studio offers a "Lifetime package. The Lifetime package means that once a family buys this package, they are permanently in this state. Market research shows that the only families that will buy the Lifetime package are ones that bought the deluxe package the year before, but only 3% of them. Research also shows that this is a tougher market than the first one. If a family did not purchase a portrait package last year, then there is a 7% chance that they will buy a regular package, and a 2% chance that they will buy a deluxe package. If a family purchased a regular package last year, then there is a 50% chance that they will not purchase a package this year, but a 12% chance that they will buy a deluxe package. If a family purchased a deluxe package last year, there is a 25% chance that they will not buy a package this year, a 32% chance that they will buy a standard package, and we already mentioned that there is a 3% chance that they will buy the Lifetime package. (a) Construct a matrix of transition probabilities for this scenario. (b) Suppose the studio has a grand opening this year. What will the percentages of the different packages bought in the 12th year be? Round the percents to two decimal places. Interpret your answers using complete sentence(s). (c) What is the steady state solution? Is this reasonable for this scenario? Explain using complete sentence(s)