Sample Question #56 (probability theory)

Can you state the Law of Large Numbers in plain English? Can you write down its formal definition?

(Hint: there are actually two versions of this "law")

(Comment: all too often, practitioners take the Law of Large Numbers for granted in carrying out empirical investigations, sometimes resulting in laughable consequences)

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ANSWER

The law of large number says that when you have a sufficiently large sample, the sample’s mean (average) is representative of the theoretical population’s mean (expectation).

The weak version says that as sample size increases, the sample mean converges to population mean in probability.

The strong version (which of course covers the weak case) states that as sample size increases, the probability of the sample mean equalling the population mean approaches 1.