Understanding common sampling distributions

A sampling distribution is a probability distribution of a sample statistic based on many samples drawn from a population. In other words, it is the distribution of a particular statistic (such as the mean, median, or proportion) calculated from many sets of samples from the same population, where each set has the same size. There are two things to take note of here. First, the sampling distribution is not about the random samples drawn from the PDF. Instead, it is a distribution that’s made from an aggregate statistic, which comes from another distribution drawn from the PDF. Second, we would need to sample from the PDF in multiple rounds to create the sampling distribution, where each round consists of multiple samples from the PDF.

Let’s look at an exercise in R to illustrate the concept of the sampling distribution using the sample mean as the statistic of interest. We will generate samples from a population whose distribution...