Sannsynlighetstettheten
Sannsynlighetstettheten, known in English as the probability density function (PDF), is a fundamental concept in probability theory and statistics that describes the likelihood of a continuous random variable taking on a specific value. Unlike discrete probability distributions, which assign probabilities to discrete outcomes, the probability density function defines probabilities over continuous ranges.
Mathematically, the PDF is a non-negative function \(f(x)\) defined over the real line (or a subset thereof)
\[
P(a \leq X \leq b) = \int_a^b f(x) \, dx
\]
Key properties of the probability density function include non-negativity (\(f(x) \geq 0\) for all \(x\)) and normalization
Common examples of probability density functions include the normal distribution (bell curve), exponential, uniform, and gamma