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The 56 pages that link to Probability density function, each with the reason it gives.

• Expected valueRelated: For continuous variables, expectation integrates values weighted by the density.

• Random variableBroader topic: It represents distributions that assign zero probability to individual values but positive probability to intervals.

• Atomic orbitalRelated: The squared magnitude of an orbital wavefunction gives the electron’s spatial probability density.

• Probability distributionCompared with: A density is a representation used for some distributions, not the distribution itself.

• Lebesgue measureRelated: Continuous probability distributions often express probabilities through densities relative to Lebesgue measure.

• Normal distributionNarrower topic: The normal curve is a specific density function; probabilities come from areas beneath it.

• AreaRelated: Probabilities correspond to areas under the density curve over intervals.

• Probability measureCompared with: A density represents a measure relative to a reference measure but is not itself event probability.

• Characteristic functionCompared with: A density gives probabilities locally, while a characteristic function encodes the whole distribution in frequency space.

• CalculusRelated: Integration converts continuous probability densities into measurable probabilities.

• Likelihood functionRelated: For continuous data, likelihood uses the density at the observed value, not the probability of that exact value.

• Indicator functionCompared with: A density measures probability through integration; an indicator only marks membership.

• Probability spaceCompared with: A density represents probabilities in a chosen coordinate space, rather than defining the full abstract space.

• Cumulative distribution functionCompared with: A density describes local probability concentration, while a CDF gives accumulated probability.

• Definite integralRelated: Definite integrals turn continuous probability densities into event probabilities.

• Improper integralRelated: Densities on unbounded supports must have a finite total integral to define probability distributions.

• Fundamental theorem of calculusRelated: The theorem helps calculate probabilities from continuous densities and their antiderivatives.

• Riemann integralRelated: Riemann integration computes probabilities when a density is suitably integrable.

• Probability mass functionCompared with: Unlike a mass function, a density's value at one point is not the probability of that point.

• Moment-generating functionRelated: For continuous variables, integrating the exponential against a density computes the function.

• Maxwell–Boltzmann distributionNarrower topic: The curve gives probabilities over speed or energy intervals, not at a single exact value.

• Lp spaceRelated: Lp membership measures the integrability and size of probability densities.

• Exponential distributionNarrower topic: The exponential density assigns probabilities to ranges of waiting times.

• Fubini's theoremRelated: For joint densities, Fubini connects integration over a region with successive marginal calculations.

• Wave functionRelated: The squared magnitude of a position-space wave function defines this density.

• Radon–Nikodym theoremBroader topic: When a probability law is absolutely continuous, its density is a Radon–Nikodym derivative.

• Cauchy distributionNarrower topic: The Cauchy distribution is specified by a density with a distinctive inverse-quadratic shape.

• Beta distributionNarrower topic: The beta distribution’s shape is specified by its probability density.

• Gaussian distributionNarrower topic: The Gaussian density assigns probability across the real line, though probability at any single point is zero.

• Integral calculusRelated: Integration turns probability densities into event probabilities.

• Order statisticRelated: For continuous samples, densities of ranked values follow from the parent density and rank.

• Probability amplitudeCompared with: A wavefunction's squared modulus is a density, whereas the wavefunction itself is an amplitude.

• Histogram (statistics)Related: For unequal bin widths, bar area—not height alone—can represent probability.

• Independent random variablesRelated: For variables with a joint density, independence is equivalent to density factorization almost everywhere.

• Absolute continuityRelated: A cumulative distribution built from a density is absolutely continuous.

• Indefinite integralRelated: Finding a cumulative distribution can require an antiderivative of the density.

• Integrable functionRelated: A density is an integrable function normalized to have total mass one.

• Particle in a boxRelated: The squared magnitude of each box wavefunction gives the position distribution.

• Chi-squared distributionRelated: Its formula shows how the distribution’s density changes with degrees of freedom.

• Dirichlet distributionRelated: The Dirichlet density specifies relative probability across the simplex.

• Log-normal distributionNarrower topic: Its density is asymmetric, with a long tail toward large positive values.

• Maximum a posteriori estimationRelated: For continuous parameters, MAP commonly maximizes posterior density rather than point probability.

• Multiple integralRelated: Multiple integrals compute probabilities for joint distributions across multidimensional regions.

• Multivariate normal distributionRelated: For a nonsingular multivariate normal, it is an exponential of a covariance-weighted squared distance.

• Real-valued functionBroader topic: It assigns real-valued densities to possible outcomes, rather than probabilities to individual points.

• Tonelli's theoremRelated: Tonelli permits marginal densities to be computed by integrating a joint density in either order.

• Lebesgue decomposition theoremRelated: The absolutely continuous part of a probability law has a density of this kind.

• Volume integralRelated: Integrating a spatial density over a three-dimensional region gives its probability.

• Outcome (probability)Compared with: Continuous models do not generally assign positive probability to individual outcomes.

• Continuous uniform distributionNarrower topic: The distribution is defined by a density that stays constant across its interval.