I'm talking about notation that I see in my stats book that looks like the notation here: https://en.wikipedia.org/wiki/Probability_density_function#Absolutely_continuous_univariate_distributions

For the second and third equations, how do you "say" those? The first thought is "f x of x", but that feels awkward as it doesn't distinguish between pdf and cdf, or between random variable and, um, is lowercase x the "event"?

Just looking for a way to verbalize these so that I'm not just looking at it and thinking "oh yea, that one"

I would just say "distribution function" and "density function", or just cdf and pdf. Trying to verbally dictate the notation gets awkward
if I am being lazy or don't need to be precise, I say "f x of x" or "big F x of x"

if I need to be more clear, I say "pdf of x" and add "evaluated at x" / "realized at x" if needed. often it is clear what RV you are talking about, so you can just say "pdf at x". I would call little x the realization of the random variable denoted by big X.
Mostly just say the letters pdf, pmf, cdf. Would also say 'density function', 'mass function', distribution function', or sometimes just 'density'.
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Not the most precise but close enough for anyone who's taken a prob/stats course: The cumulative density function is defined as the integral from -inf to x of the probability density function f_x.

The PDF is defined as the derivative of the CDF with respect to x.

You could use more formal language but I think by doing so you'd be missing the fact that these 2 equations are just definitions. The derivative of a CDF is a PDF, and the integral of the PDF is its CDF.

I don't know if you would call them axioms or not, but they're almost like saying that the probability of the space must sum to 1. You can say it in a much more complex way but at the end of the day that's all it'll ever really mean.
I might say “capital F sub X evaluated at lower case x” or something like that. I’m curious to hear what other people say.
Would it be wrong to say X Function evaluated at x? (It's what we say in my language but unsure if it fits in English. It sounds like X would be the name of a function in English, which isn't what they mean here)
If it's obvious which of f or F you would mean by context (e.g. I just mentioned a density), I'd just say "f x of x" but if not I'd say "little f" or "big F" as needed.

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