Category Archives: Mathematics

Simulation of the Law of the Large Numbers


Simulation is important to develop our intuitive understanding. So when the difficult content appears, try considering a sample. If there’s no handy sample, creating a sample with R is very efficient, simulation in other words.

When we want to understand the law of the large number, we can also generate it virtually. Here, I will show you the simulation. Consider the function which takes (x in [0, 3)) and the value is in ([0, 1)), such as ( g(x) = frac{1}{4} x(3-x)(x-0.75)^2). ((g(x)) can’t be a density function for the random variable, because (int _0 ^1 g(x) dx neq 1). It is the probability to admit (x) value generated by randomly. It is for creating trial data.)

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[Simulation] the Law of Large Numbers and the Central Limit Theorem


Seeing samples, simulation in other words, is a good way to understand the concept, so I’ll explain with an example. At first, I’ll show the explanation of the law and theorem, and then I’ll provide the example.

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Similarity among Binomial, Poisson and Normal Distributions


Binomial Distribution (textrm{Binomial}(m, p)) is similar to Normal and Poisson distributions.

Especially (n) is large, it can be approximated as a normal distribution, according to the central limit theorem.

Let’s see the similarity with graphics.

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