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Law of Large Numbers?
Basically, the sample mean x̄ = (1/n)Σ(Xᵢ) tends to population mean µ, as the sample size n tends to infinity.
I understand the concept in layman's terms. However I don't quite understand the math description:
What in the world is this epsilon? I would think |x̄ - µ| = 0, not 1
"We say x̄ converges in probability to µ", o....o So the probability x̄ = µ = 1?
2 Answers
- MorningfoxLv 71 year agoFavorite Answer
The standard reading is that "P" stands for probability. It is the probability that equals 1, which is the same as 100%. In the limit, the probability that | x̄ - µ | is smaller than any number you pick epsilon > 0, is equal to 1. You can pick epsilon = 0.1, or 0.001, or 0.0000001 ... it doesn't matter. For a large enough value of "n", the difference between x̄ and µ is going to be smaller than the number you picked.
On the other hand, you might need to use a VERY large value of "n". That's where the fun begins.
