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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"

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I would just say "distribution function" and "density function", or just cdf and pdf. Trying to verbally dictate the notation gets awkward
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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.
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Mostly just say the letters pdf, pmf, cdf. Would also say 'density function', 'mass function', distribution function', or sometimes just 'density'.
by
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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.
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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.
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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)
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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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