4.1 Simple Random Sample

SW 2.5

Let’s start by talking about how the data that we have access to is collected. There are several possibilities here, but let us start with the most straightforward case (which is also a very common case) called a simple random sample.

In math: \(\{Y_i\}_{i=1}^n\) is called a simple random sample if \(Y_1, Y_2, \ldots, Y_n\) are independent random variables with a common probability distribution \(f_Y\). The two key conditions here are (i) independence and (ii) from a common distribution. For this reason, you may sometimes see a random sample called an iid sample which stands for independent and identically distributed.

In words: We have access to \(n\) observations that are drawn at random from some underlying population and each observation is equally likely to be drawn.