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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.

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

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

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

• 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.

• 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.

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

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

• 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.

• 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.

• 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.

• 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.

• 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.

• 68–95–99.7 ruleRelated: The rule’s percentages are areas beneath the normal probability density.

• Family (statistics)Related: A shared density form often defines how family members relate.

• Jacobian matrix and determinantRelated: Changing random-variable coordinates transforms densities by an absolute Jacobian determinant.