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Theory of Large Numbers

Theory of Large Numbers

The theory of large numbers is widely applicable in statistics and probability. It describes the results obtained when the same experiment is repeated a number of times. The theory states that ‘when the same experiment or study is repeated independently for several times, the average of the results of the trials should be close to the expected value”. In other words, the results moves closer and closer to the expected outcome, as the number of trial is increased. This theory is considered significant in statistics because it shows that long-term and stable results could be obtained from the random events. It is important to note that the theorem deals with a large number of experiments. Each additional experiment contributes to the increase of precision towards the average results.

Example of theory of large numbers

A perfect example of the theory of large number is rolling of a dice. The roll of a dice has six different events having equal probabilities of occurrence (1/6). Therefore, the expected value of the roll of a dice could be represented as follows.

Lets say we roll a dice for three times and we get the results as 6, 6, 3. Then the average of this results will be 5, which is quite far away from the expected value of 3.5. however,  if we roll the dice for four times and we ger the results as 5, 2, 6, and 4, then the average would be 4.75, which is closer to expected results of 3.5. However, it the dice is rolled for 6 times and the results is gotten to be 2, 6, 4, 3 and 1, the average would be 3.2, which is more closer to the expected value.

Application of theory of large numbers

The concept of theory of large numbers is applied in business and finance, from the concept of growth  rates of businesses. In this case, the law indicates that as the company grows, it continuously becomes quite difficult to maintain its previous growth rates. Therefore, the growth rate of the company declines as the company grows. Additionally, various metrics applies the law of large numbers, such as net income, market capitalization and revenue. For instance, lets consider two companies. Company ABC market capitalization is $1 million while company XYZ market capitalization is $100 million. ABC has a market growth of 50% per annum and it finds it easy to attain its growth rate because its market capitalization grows only by $500,000. However, for company XYZ, its almost impossible to attain its market capitalization because it have to grow with $50 million.