S3. The Law of Large Numbers and the Central Limit Theorem

Question 1

Define the Law of Large Numbers

Answer 1

As the sample size grows, the sample mean converges, in a certain sense, with the population mean.

Question 2

Define the Central Limit Theorem

Answer 2

As the sample size grows, the distribution of the standardised sample mean converges to a standard normal i.e. N(0,1).

Question 3

How is the Law of Large Numbers written mathematically?

Answer 3

Question 4

How is the Central Limit Theorem written mathematically?

Answer 4