What is the difference between the Law of Large Numbers and the Central Limit Theorem?
- Both are essentially the same.
- The Central Limit Theorem is a law, while the Law of Large Numbers is a theorem.
- The Law of Large Numbers is used for calculating probabilities, while the Central Limit Theorem is used for integration.
- The Law of Large Numbers states that as a sample size increases, the sample mean approaches the population mean, while the Central Limit Theorem states that the distribution of sample means approximates a normal distribution as the sample size increases.
The Law of Large Numbers and the Central Limit Theorem are both key concepts in probability and statistics, but they say different things. The Law of Large Numbers states that as the size of a sample is increased, the sample mean will get closer to the population mean. The Central Limit Theorem, on the other hand, states that as the sample size increases, the distribution of sample means approaches a normal distribution.
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