Apple Inc.

Apple Inc. is an American multinational corporation that designs and manufactures consumer electronics and computer software products. The company operates more than 393 retail stores in fourteen countries as of August 2012, and an online store where their hardware and software products are sold. It also includes stores such as the iTunes and App store online that enables users of products to purchase new systems and programs, called ‘Applications’ or download music. My own father is a big fan of the company and fully supports its activities. He often discusses to me the topics related to its success, predicting the company’s future status and importance to the world. Due to this, I held an interest for the company, often updating myself with news on business sites, wondering whether Apple Inc. will ever be overthrown by another brand or company.
Found on April 1, 1976 and then incorporated on January 3, 1977, Apple is currently one of the world’s largest mobile phone manufacturers, rivalling big brands such as Samsung and Nokia. The company is best-known for its hardware products which include; the Mac line of computers, the iPods, iPhones and iPads. They release new products almost every second year from their lines of products through research and development to improve the hardware as well as its software. It is listed as the largest publicly traded corporation in the world by market capitalization, with an estimated value of US$626 billion as of September 2012. The Apple market cap is larger than that of successful companies such as Google and Microsoft combined. Its worldwide annual revenue in 2010 totalled $65 billion, growing to approximately $156 billion in 2012. Apple Inc. is currently worth within the top 10 companies of the world.
For the exploration report I have compiled a survey for a number of students at the Queensland Academy of Science, Maths and Technology (QASMT) that helped gather raw data to then mathematically calculate the percentage that prefers Apple Inc. over other brands. Using the Markov Chain procedure, the state of change for every two years (according to the average time it takes for Apple to release a new product) is then calculated and converted into percentage. With 20 students in total surveyed, the results will be compared to the world’s population. Due to number being too small and the age group limited to one, the calculations and all results should not be taken into consideration for the actual status (or rank) of the company.

Survey
For the survey, two questions were necessary to create the Markov chain; Do you own a smartphone? If so, what brand? If you had a choice, which brand/smartphone would you prefer to use?
This was sent in email form to random students of QASMT, and the results were place in a more organised order:
Table 1. Results of survey on smartphone brands
Question 1 Question 2
Apple Apple
Apple Apple
Apple Apple
Apple Apple
Apple Apple
Apple Apple
Apple Apple
Apple Apple
Other Apple
Other Apple
Other Apple
Other Apple
Apple Other
Apple Other
Apple Other
Other Other
Other Other
Other Other
Other Other
Other Other
*names not included for privacy purposes

Markov Chain
Named after Andrey Markov, the Markov chain is a mathematical system that uses matrix to present transitions from one state to another; this can also be known as the state of change. It is a stochastic process or random process which is made up of a collection of random variables. Usually a Markov chain is defined for a discrete set of times. A discrete-time stochastic process involves a system which is in a certain state at each step, with the state changing randomly between steps. The Markov property states that the conditional probability distribution for the system at the next step (and in fact at all future steps) depends only on the current state of the system, and not additionally on the state of the system at previous steps.