Implied meaning of lower case latin letters $p$, $q$, $u$ etc. in probability?

Question

Are there any generalizations that should be assumed for (lower case) $p$, $q$ and $u$ in probability theory? For example, $q$ is often assumed to signify, in relation to $p$, that $$ q=1-p. $$ Is there a standard implied meaning/relation that should be made (unless stated otherwise) when encountering these lower case letters and and if so, what are the most common ones and their meaning/relation in a probabilistic setting?

EDIT: To clarify my question, I am interested in the implied meaning and/or relation of the lower case letters from the modern Latin alphabet such as $u$, not general notation practices with Greek symbols etc, in probability theory.

Answer 1

In general, one should not rely on notation to be common across the literature, but nonetheless conventions exist. Here are a few that I am aware of:

General

• $i,j,n,m,k,l \in \mathbb{N}$ indices

Probabilistic Setting

• $\mu = \mathbb{E}[X]$: mean of a random variable $X$
• $\sigma = \text{Var}[X]$: variance of a random variable $X$
• $\Sigma = \text{Cov}(X)$: covariance matrix of a multivariate random variable $X$
• $\rho = \text{corr}(X,Y)$: correlation
• $r$: sample Pearson correlation coefficient
• $\theta$: parameter of a distribution
• $p$: probability mass function or probability density
• $f$: probability density
• $F$: cumulative density function
• $\phi$: characteristic function

Note: The letter $i$ is a good example of notation being used in different settings. It is often used to denote indices, but in a probabilistic setting in particular when using characteristic functions it refers to the imaginary unit.