Law of Large Numbers
The — says that if we observe more and more trials of any random process, the proportion of times that a specific outcome occurs approaches its probability.
The Law of Large Numbers is a statistical concept that describes how the average of a large number of repeated independent experiments will converge towards the expected value of the distribution as the number of trials increases. This law is a fundamental principle of modern probability theory and has applications in many fields, including finance, physics, and economics.
The law states that as the number of trials increases, the average of the outcomes will become more stable and closer to the expected value of the distribution. This means that if a coin is flipped many times, the percentage of heads will eventually approach 50%, which is the expected value.
The Law of Large Numbers plays an important role in making statistical inference because it helps to determine the reliability and accuracy of statistical estimates. This law is particularly relevant when estimating parameters such as the mean and variance of a population where only a sample can be observed.
Overall, the Law of Large Numbers is a crucial aspect of probability theory and statistics that provides a theoretical foundation for many practical applications.
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