The weak law on large numbers
The questions from the previous section led us to limit theorems. The most important limit theorems are the (weak) law of large numbers, the theorem of (Glivenko, 1933) and (Cantelli, 1933), and the central limit theorem.
First we will have a look at the weak law of large numbers. The strong law of weak numbers is mathematically more sophisticated, but tells (almost) the same story.
The weak law of large numbers is a very intuitive concept; Jakob Bernoulli even thought this 20 years after he published it in 1713, as the golden theorem. But if we take a closer look at this law, we jump into a whole world of mathematical statistics.
The weak law of large numbers is applied in betting offices, in financial assessments and for insurance, and so on. It builds the foundation of statistics, and data scientists should be aware of it. By understanding the weak law of large numbers and the central limit theorem, one understands the basics of mathematical statistics.
