What Law of large numbers is
The Law of Large Numbers is a theorem in probability theory that states that as the number of trials or observations increases, the average of the results will converge to the expected value. This theorem is also known as the law of averages.
The steps for the Law of Large Numbers are as follows:
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Calculate the expected value of a random variable.
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Take a large number of samples of the random variable and calculate the average of each sample.
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Compare the average of each sample to the expected value.
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As the number of samples increases, the average will approach the expected value.
Examples
- Insurance companies use the law of large numbers to calculate their expected losses on a given policy.
- Casinos rely on the law of large numbers to ensure that their expected profits remain consistent over time.
- Market analysis firms use the law of large numbers to assess the future performance of stocks and other investments.
- Economists use the law of large numbers to analyze the inflation rate and other macroeconomic indicators.
- Polling organizations use the law of large numbers to ensure that their survey results are accurate and reliable.