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Hands-on Tutorial
The Statistics Simulation of Central Limit Theorem and Law of Large Number
The basic theory and tutorial on how to simulate the central limit theorem and law of large numbers using R
Getting started with Statistics simulation using R
In Statistics, the central limit theorem and law of a large number have an important role, for instance in hypothesis testing. The central limit theorem states that the sample means will be normally distributed, it doesn’t depend on the population distribution, skewed or not. In this tutorial, we will learn the simulation using 5 different distributions.
Central limit theorem
The central limit theorem states that the distribution of the sample means will be normally distributed in which the population mean is μ and the standard deviation is σ when we take the large random samples from the population (with replacement).
According to J. Orloff and J. Bloom (2014), suppose X1, X2, X3,…, Xn are the i.i.d random variables with a mean μ and standard deviation σ.
The properties of mean and variance are as follows.
