Law of Large Numbers (If m = the sample size and M is the population size...)

[Agent Smith]

Just watched a video on Law of Large Numbers. Says the creator ...

"for some random variable [imath]X[/imath], for [imath]n[/imath] observations of [imath]X[/imath] in [imath]n[/imath] samples, as [imath]n \to \infty[/imath], [imath]\overline X \to \mu[/imath], where [imath]\mu = [/imath] the population mean." This be the law of large numbers.

So far so good?

I was wondering about this though ...

If m = the sample size and M is the population size, for 1 sample, [imath]m \to M \implies \overline x \to \mu[/imath]. The larger the sample size, the better it is, oui, statistically?

Is this also a law with a name or does it simply get clubbed under A good sample (should be ...)?

 

[Agent Smith]

I would like some help ... please

 

[blamocur]

Just watched a video on Law of Large Numbers. Says the creator ...

"for some random variable [imath]X[/imath], for [imath]n[/imath] observations of [imath]X[/imath] in [imath]n[/imath] samples, as [imath]n \to \infty[/imath], [imath]\overline X \to \mu[/imath], where [imath]\mu = [/imath] the population mean." This be the law of large numbers.

So far so good?

I was wondering about this though ...

If m = the sample size and M is the population size, for 1 sample, [imath]m \to M \implies \overline x \to \mu[/imath]. The larger the sample size, the better it is, oui, statistically?

Is this also a law with a name or does it simply get clubbed under A good sample (should be ...)?

I am not sure your statement is correct -- would you care to prove it?

 

[Dr.Peterson]

I was wondering about this though ...

If m = the sample size and M is the population size, for 1 sample, [imath]m \to M \implies \overline x \to \mu[/imath]. The larger the sample size, the better it is, oui, statistically?

Is this also a law with a name or does it simply get clubbed under A good sample (should be ...)?

Have you thought about it?

With a finite population, what happens as the sample size goes to infinity? (Can it?)

The LLN is not about a population, but a random variable.

 

[Agent Smith]

Have you thought about it?

With a finite population, what happens as the sample size goes to infinity? (Can it?)

The LLN is not about a population, but a random variable.

Correctamundo, that seems to be the case. I get confused between Law of Large Numbers and Central Limit Theorem. Both, it seems, are about the number and not size of the samples. Is the former about the mean of the sample means approaching the population mean and the latter about the distribution of the samples approaching a normal distribution?