Law of large numbers

You might have definitely learned the theory of probability in Mathematics. Probability theory comprises of law of large numbers. It is a theorem that will be describing that how the same experiment can be performed many times. As per this law, average results that are obtained from the trials should match with the expected value. If they are not closer to expected value then you will be required to repeat the number of trials. This can be easily explained with the help of an example- if you are rolling a dice then it will be producing one of the six numbers and all the numbers will have an equal probability. So if you add all the numbers and then divide it by six then you will find that probability will be 3.5. If you go through this theory then you will find that all the large numbers have a probability of being close to number 3.5. This closeness to this number can also be increased as you roll the more number of dices. According to the theory of large numbers, Bernoulli trials will be equivalent to theoretical probability.

In a Bernoulli variable expected value is equivalent to theoretical probability. Average of such n number of variables will be precisely its relative frequency. For instance- if you are tossing a coin then it is referred to as Bernoulli trial. If you do the flipping of a coin then you will find that outcome of the heads is equivalent to one by two. This rule is according to the theoretical probability. Most of all the mathematicians and researchers make use of this large numbers theory. The reason behind this is that this large numbers theory guarantees a very stable and long term results for all the random events. You can also take the example of a casino. In a casino, you can lose the money by just one spin of roulette wheel. Now, you will be in a position to predict your earnings and these earnings will tend to move the predictable percentages over the number of spins that you do.

You should always keep in your mind that this theory of large numbers will be used only when you are making the use of very large observations. This theory of large numbers was proved by a Swiss mathematician Bernoulli Jakob. Bernoulli was the first person to prove this theory. This theory was proved in year 1713. According to Bernoulli, every game can be played with endless number of repetitions and all the games will be having only two possible outcomes. These outcomes are either you win or either you lose. This theory was later on proved by another mathematician of Russia Pafnuty Chebyshey. This theory is very much similar to that of averages law. About twenty years were taken by Bernoulli in order to prove this theory. Initial name that was given to this theory was golden theory and later on name was changed to Bernoulli theory. You should definitely study the weak law as well as strong law along with this law of large numbers.