🎲  Probability Density

Probability Density#

The relative likelihood of a continuous variable at a value, given by its PDF.

Important

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What it is#

The probability density function (PDF) \(f(x)\) describes a continuous random variable. It is not a probability itself — its area is: the probability of landing in an interval is the integral

\[P(a \le X \le b) = \int_a^b f(x)\,dx.\]

Properties#

The density satisfies \(f(x) \ge 0\), may exceed 1 (it is a density, not a probability), integrates to one over the whole line, and assigns probability zero to any exact value. The bell curve of the normal distribution is the classic PDF.