The Law of Large Numbers is a fundamental principle in probability theory and statistics that describes how the average of results obtained from repeating an experiment many times will converge to the expected value. Think of it as nature's way of revealing its true probabilities through repeated observations.
"As the number of trials increases, the experimental probability approaches the theoretical probability."
Consider a sequence of independent and identical trials with expected value . The sample average is:
As the number of trials () approaches infinity:
This means the probability that our sample average differs from the true mean by any small amount () approaches zero as we increase our sample size.
The Law of Large Numbers is a fundamental principle in probability theory and statistics that describes how the average of results obtained from repeating an experiment many times will converge to the expected value. Think of it as nature's way of revealing its true probabilities through repeated observations.
"As the number of trials increases, the experimental probability approaches the theoretical probability."
Consider a sequence of independent and identical trials with expected value . The sample average is:
As the number of trials () approaches infinity:
This means the probability that our sample average differs from the true mean by any small amount () approaches zero as we increase our sample size.
