Thread: The Strong Law of Large Numbers

Can somebody in basic terms-for I have never studied probability- explain what the "Strong Law of Large Numbers" as well as "Weak Law of Small Numbers".

Originally Posted by ThePerfectHacker

Can somebody in basic terms-for I have never studied probability- explain what the "Strong Law of Large Numbers" as well as "Weak Law of Small Numbers".

The Law of Large Numbers says that the long-time sample mean of a series of independent observations approaches the theoretical mean of a single observation. That is, the sample mean ( a random quantity) becomes deterministic in the limit of large samples. It connects axiomatically based probability theory back to the frequentist definition of probability, an older approach.

I remember in College statistics we learned never to have a sample larger than 10% of the poulation. Why is that? Does it have anything to do with the aforementioned theory?

Originally Posted by MathGuru

I remember in College statistics we learned never to have a sample larger than 10% of the poulation. Why is that? Does it have anything to do with the aforementioned theory?

Indirectly, yes. If your sample size is too large relative to the population, the members of the samples are "too dependent" (since you won't use the sample population member twice, your population changes as you are sampling). Then most of the usual theory becomes inapplicable. However, the LLN really only applied to cases where you can repeat a random experiment as many times as you want. So for a finite population, this works only if you are willing to sample the same member of the population more than once (sampling with replacement).

I found it interesting that people used The Strong Law for millenia by observing patterns in nature without really understanding why it is thus.
Why is the Strong Law an important law in probabilty theory?

Originally Posted by ThePerfectHacker

I found it interesting that people used The Strong Law for millenia by observing patterns in nature without really understanding why it is thus.
Why is the Strong Law an important law in probabilty theory?

Because modern probability theory is axiomatic and not a priori concerned with reality. The LLN (any version, there are many) allows a connection back to reality.