Agent Smith
Junior Member
- Joined
- Oct 18, 2023
- Messages
- 84
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 ...)?
"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 ...)?