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Mathematics · Glossary

What is Density, continuous random variable?

Also known as: density

Definition 35.1 High School Mathematics · Chapter 35 — Continuous Random Variables

A probability density on an interval II is a continuous, nonnegative function ff on II with ∫If(t)  ⁣dt=1\int_I f(t)\,\dd t = 1 (the integral over an unbounded II being understood as a limit of integrals over growing bounded intervals). A random variable XX has density ff if for all a≤ba \leq b in II:

P(a≤X≤b)=∫abf(t)  ⁣dt.\P(a \leq X \leq b) = \int_a^b f(t)\,\dd t .
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