The Law of Large Numbers (LLN) tells us that when we do more and more trials or take more samples, the average of those samples will get closer to what we expect.
For example, if you flip a coin many times, the number of heads you get will be around half of the total flips. This means you can expect about 50% heads and 50% tails.
Now, the Central Limit Theorem (CLT) is another important idea. It says that no matter how the original data looks, when we take enough samples, the average of those samples will start to look like a normal bell-shaped curve.
This is helpful because it means we can use regular probability methods, even if the original data isn't normal.
In short, the LLN helps us understand that averages become stable as we collect more data. The CLT helps us make predictions about those averages, which is really important in statistics.
The Law of Large Numbers (LLN) tells us that when we do more and more trials or take more samples, the average of those samples will get closer to what we expect.
For example, if you flip a coin many times, the number of heads you get will be around half of the total flips. This means you can expect about 50% heads and 50% tails.
Now, the Central Limit Theorem (CLT) is another important idea. It says that no matter how the original data looks, when we take enough samples, the average of those samples will start to look like a normal bell-shaped curve.
This is helpful because it means we can use regular probability methods, even if the original data isn't normal.
In short, the LLN helps us understand that averages become stable as we collect more data. The CLT helps us make predictions about those averages, which is really important in statistics.