Mindy and Gemma own two different mobile phone companies. Mindy's company is called Windy Service (W)...

 

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Mindy and Gemma own two different mobile phone companies. Mindy's company is called Windy Service (W) and Gemma's, My Gem (G). At the moment Windy Service owns 15% and My Gem 40% of the market share. The rest is owned by other companies (C). The girls decide to promote their companies by advertising their product. As a result their accountants have made the following predictions. If a person is using Windy Service in a particular year, there is a 5% chance they will switch to other companies and a 2% chance they will switch to My Gem in the following year. If a person is using My Gem in a particular year, there is a 4% chance they will switch to Windy Services and a 10% chance they will switch to other companies in the following year. If they use another company in a particular year, there is a 15% chance they will switch to My Gem and 12% chance they will switch to Windy Service in the following year. a. Complete the initial state matrix below, expressing the percentages as proportions; for example 70% = 0.7. 1 mark W S= G C b. Write down the transition matrix, expressing the percentages as proportions. This year WGC W 1 mark = G Next year C After surveying the population, the accountants decided to adjust their predictions. Use the following transition matrix T, to answer the questions below. This year W G C [0.8 0.2 0.2 W T= 0.1 0.7 0.3 G Next year 0.1 0.1 0.5 C c. What is the predicted market share after one year of advertising? d. What is the predicted market share after four years of advertising? Give your answers correct to three decimal places. e. What is the market share after 50 years? Give your answers as a percentage correct to one decimal place. f. Which company is predicted to do the best? Mindy and Gemma own two different mobile phone companies. Mindy's company is called Windy Service (W) and Gemma's, My Gem (G). At the moment Windy Service owns 15% and My Gem 40% of the market share. The rest is owned by other companies (C). The girls decide to promote their companies by advertising their product. As a result their accountants have made the following predictions. If a person is using Windy Service in a particular year, there is a 5% chance they will switch to other companies and a 2% chance they will switch to My Gem in the following year. If a person is using My Gem in a particular year, there is a 4% chance they will switch to Windy Services and a 10% chance they will switch to other companies in the following year. If they use another company in a particular year, there is a 15% chance they will switch to My Gem and 12% chance they will switch to Windy Service in the following year. a. Complete the initial state matrix below, expressing the percentages as proportions; for example 70% = 0.7. 1 mark W S= G C b. Write down the transition matrix, expressing the percentages as proportions. This year WGC W 1 mark = G Next year C After surveying the population, the accountants decided to adjust their predictions. Use the following transition matrix T, to answer the questions below. This year W G C [0.8 0.2 0.2 W T= 0.1 0.7 0.3 G Next year 0.1 0.1 0.5 C c. What is the predicted market share after one year of advertising? d. What is the predicted market share after four years of advertising? Give your answers correct to three decimal places. e. What is the market share after 50 years? Give your answers as a percentage correct to one decimal place. f. Which company is predicted to do the best?