Question

Is the law of large numbers a phenomenon? If something is random, then how can we define an average outcome?

Answer 1

Hint: We are required to explain what is meant by the law of large numbers. This is a very important concept in statistics which helps us to determine the outcomes of random events with a large number of trials. These results are stable. Suppose we have the inputs of any event which is random, we can calculate the average outcome using the Law of Large numbers which is in accordance with the Law of Averages.

Complete step-by-step solution:
Law of Large numbers is a statistical concept key to determine the outcomes of many events. In statistics, this law of large numbers is a law used to determine the output of an event which is conducted with a large number of trials. This law helps us to calculate the average outcome for an event with random tries. This result is quite close to the expected value.
Using this concept, we can say that the results produced are quite stable and pretty accurate. Now let us assume a case where there is a large number of random events occurring, for example just the rolling of a dice. If we roll this dice a large number of times, it is pretty obvious that certain patterns can be observed. Once we are able to make note of these patterns, we can easily determine the average outcome by using statistical formulae. So, using this concept, we can say that the output of this law produces an output which becomes more and more stable as well as accurate. As the number or random events taking place increases, the average value obtained becomes that much closer to the expected value.
This Law of Large numbers is somewhat similar to the Law of Averages. The difference between them is that the Law of Averages is not a mathematical principle whereas the Law of Large numbers is a mathematical principle.

Note: It is important to know the concepts of statistics and probabilistic approaches to solve such questions. We need to note that the law of large numbers is valid only in the case where a large number of trials are conducted. Otherwise, it does not hold good.