5  Random Variables and Random Samples

Imagine this morning you are assigned 10 new patients at the clinic. For each patient, you record the number of decayed teeth.

Patient 1 has 0.

Patient 2 has 2.

Patient 3 has 4.

Patient 4 has 1.

… and so on.

Before you actually examine each patient, you do not know how many decayed teeth you will find. It could be 0, it could be 5, it could be 8. That uncertainty about the outcome is what we formalize as a random variable.

6 Random Variable (\(X\))

Let’s define \(X\) as the number of decayed teeth in a single patient.

Each patient has their own value of \(X\), but before examination we dont know what that is.

This uncertainty is called the random variable.

7 Random Sample

Now, when we see 10 patients and record each of their numbers, we get a random sample:

\((X_1, X_2, X_3, \ldots, X_{10})\)

Each \(X_{i}\) is the same kind of measurement (decayed teeth count), just for a different patient. Taken together, that’s our data.”

Random variables can be discrete or continuous.

Discrete values are absolute values mostly integers but it is important to be cautious about the stable, but random ordinal values.