law of large numbers
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 principle that describes the behavior of the average of a large number of independent random variables. According to this principle, as the number of trials or observations increases, the average of these variables will converge to the expected value or mean of the distribution from which the variables are drawn.
In other words, the law of large numbers states that the more times you repeat an experiment or observation, the closer the observed values will be to the expected value or true value of the population. For example, if you flip a coin 10 times, you might get 6 heads and 4 tails, which is not necessarily representative of the true probability of the coin. However, if you flip the coin 10,000 times, the average number of heads and tails will converge to 50-50, which is the expected probability for a fair coin.
The law of large numbers is important in statistics and probability because it allows us to make predictions and infer conclusions about a population based on a sample. It also underlies many statistical tests and methods, such as the central limit theorem and hypothesis testing, which rely on the assumption of large sample sizes and the convergence of sample statistics to population parameters.
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