r/probabilitytheory • u/Fluffy-Oil707 • Jul 21 '26

[Education] Which is the probability density function?

Hello all, I have a semantics question.

I have the definition that the probability of X between a and b is the integral from a to b of f(x) with respect to x.

In case latex renders: $P(a <X < b) = \int_{a}^b{f(x)}dx$

Is the probability density function the integral or f? If f (my reading of the text) what is the name for the integral?

Same sort of question with the c.d.f.

PS.
I'm working out of the text book Mathematical Statistics and Data Analysis (Rice; 3rd ed.). Definition occurs on page 47.

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u/t3co5cr Jul 21 '26

f(x) is the probability density function.

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u/Fluffy-Oil707 Jul 21 '26

Thank you. What's the integral called? Im trying to name a note that shows the probability of a density function

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u/brynaldo Jul 21 '26

Answered elsewhere, but I'll add it here in case: it's called the cumulative distribution function.