please make sure to use left stochastic matrices.
1. Finn's Fine Family Fotos is a chain of professional photography studios specializing in family portraits. They offer two kinds of picture packages: regular and deluxe. Market research shows that, if a family in the area around the studio did not have a portrait done last year, then there is an 8% chance they will by a regular package this year, and a 6% chance they will buy a deluxe package. Also, if a family purchased a regular package last year, then there is a 40% chance they will not buy a package this year, but a 10% chance they will purchase a deluxe package. And, if a family purchased a deluxe package last year, there is a 15% chance they will not buy a package this year, but a 20% chance they will buy a regular package. (a) Construct a matrix of transition probabilities for this scenario. (b) Suppose a studio has a grand opening in a community, i.e. no family used the studio last year. What percentages of families this year will not have a portrait made, will buy a regular package, will buy a deluxe package? Answer the question using full sentence(s). (c) What will the percentages be in the studio's fifth year of business? Round your percents to two decimal places (after the decimal). (d) Compute the steady state solution. Round your percents to two decimal places. Interpret the solution using complete sentence(s). (e) Suppose in the fifth year, the studio starts to give discounts to families that use the studio and that this changes only the percentages such that: if a family purchased a regular package, then there is a 10% chance that they will not return at all, but a 25% chance that they will buy a deluxe package. How will this affect the steady state solution? Round your percents to two decimal places. Interpret the solution using complete sentence(s). 1. Finn's Fine Family Fotos is a chain of professional photography studios specializing in family portraits. They offer two kinds of picture packages: regular and deluxe. Market research shows that, if a family in the area around the studio did not have a portrait done last year, then there is an 8% chance they will by a regular package this year, and a 6% chance they will buy a deluxe package. Also, if a family purchased a regular package last year, then there is a 40% chance they will not buy a package this year, but a 10% chance they will purchase a deluxe package. And, if a family purchased a deluxe package last year, there is a 15% chance they will not buy a package this year, but a 20% chance they will buy a regular package. (a) Construct a matrix of transition probabilities for this scenario. (b) Suppose a studio has a grand opening in a community, i.e. no family used the studio last year. What percentages of families this year will not have a portrait made, will buy a regular package, will buy a deluxe package? Answer the question using full sentence(s). (c) What will the percentages be in the studio's fifth year of business? Round your percents to two decimal places (after the decimal). (d) Compute the steady state solution. Round your percents to two decimal places. Interpret the solution using complete sentence(s). (e) Suppose in the fifth year, the studio starts to give discounts to families that use the studio and that this changes only the percentages such that: if a family purchased a regular package, then there is a 10% chance that they will not return at all, but a 25% chance that they will buy a deluxe package. How will this affect the steady state solution? Round your percents to two decimal places. Interpret the solution using complete sentence(s)
