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](https://improve-future.com/wp-content/uploads/2019/06/standard_normal_distribution-150x150.png "[Simulation] the Law of Large Numbers and the Central Limit Theorem")
