# Why is sample size lowercase n when we typically denote random variables as uppercase? [closed]

We have population parameters ($$\theta$$) that are NOT random variables*: $$\mu$$, $$\sigma$$, $$\rho$$, etc.

We have sample statistics that ARE random variables: $$\bar{X}$$, $$S$$, $$\hat{P}$$, etc. Since they are random variables, it is conventional to capitalize them.

It is conventional to refer to population size as $$N$$ and sample size as $$n$$.

My question is the following: Why does this stray from our classical logic of using capital letters to denote random variables? Is it because $$n$$ refers to a specific number and thus is not a random variable? I am looking for the reasoning/explanation for why this notation is used; notation is naturally subjective, but I hope someone can shed light on why this specific convention is followed.

• There are various conventions for various things, & they aren't always consistent. The convention you're referring to is more common in the survey statistics world. In other contexts, $N$ is the total number of statistical units in an experiment, & $n$ is the number per condition. In still other cases, various subscripts are used to indicate different applications. In general, while $N$ is not a parameter, I wouldn't call it either a random variable or a sample statistic. Jun 23 at 19:27