# Probability density function <!-- MICROSIMGEN:BEGIN v1.7 — generated by g08_place_microsims.py; three.js first (§15); do not hand-edit inside --> ## Microsims — p5.js ### Probability density function (p5.js) · `p(x)` <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/o1ATfTxiG" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Probability density function — p5.js microsim"></iframe> </div> *The curve whose area gives the likelihood a random variable lands in a range.* **Open in the editor:** [&#9654; fork this sketch](https://editor.p5js.org/sciencenibber/sketches/o1ATfTxiG) · movement *IX · Foundations & the rest of the toolbox* · library `p5js` ### Related microsims Live sims on neighbouring articles — 1 of them inside this article's own Wikipedia link tree: - [[Convolution]] *(in tree)* - [[Analog_signal]] - [[Autocorrelation]] - [[Bifurcation_theory]] - [[Calculus]] - [[Chaos_theory]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.* <!-- MICROSIMGEN:END --> ## Links (Wikipedia order) <!-- injected from _registry/childlinks/Probability_density_function.json (2026-07-30T02:09:12Z) --> `Absolute_continuity` · `Absolute_value` · `Almost_everywhere` · `Atomic_orbital` · `Borel_set` · [[Box_plot]] · `Cantor_distribution` · `Cauchy_distribution` · `Central_moment` · `Characteristic_function_(probability_theory)` · `Combinant` · `Continuous_or_discrete_variable` · `Continuous_uniform_distribution` · `Conversion_of_units` · [[Convolution]] · `Countable_set` · `Counting_measure` · `Cumulant` · `Cumulative_distribution_function` · `Density_estimation` · `Derivative` · `Differentiable_function` · `Dirac_delta_function` · `Encyclopedia_of_Mathematics` · `Eric_W._Weisstein` · [[Expected_value]] · `Frequency_(statistics)` · `Function_(mathematics)` · `Generalized_function` · `George_Casella` · `Home_range` · `Infinitesimal` · `Integer` · `Integral` · `Interval_(mathematics)` · `Inverse_function` · `Jacobian_matrix_and_determinant` · `Kernel_(statistics)` · `Kernel_density_estimation` · `Kurtosis` · `L-moment` · `Law_of_the_unconscious_statistician` · `Lebesgue_measure` · `Likelihood_function` · `List_of_convolutions_of_probability_distributions` · `List_of_probability_distributions` · `Main_diagonal` · `MathWorld` · `Measurable_space` · `Mode_(statistics)` · `Moment_generating_function` · `Monotonic_function` · `Multivariate_random_variable` · `Normal_distribution` · `Parameter` · `Partial_derivative` · `Patrick_Billingsley` · `Probability_amplitude` · `Probability_axioms` · `Probability_distribution` · `Probability_generating_function` · `Probability_mass_function` · `Probability_theory` · `Pushforward_measure` · `Quantile_function` · `Rademacher_distribution` · `Random_variable` · `Ratio_distribution` · `Roger_Lee_Berger` · `Sample_space` · `Skewness` · `Standard_deviation` · `Statistical_inference` · `Triangular_matrix` · `Univariate_distribution` · `Variance` > Signal Processing concept · part of the Signal Processing Portal · movement IX · !09 解析 kaiseki.svg <!-- RENDER-THUMB:START --> !480 *Rendered from the live microsim (▶ motion).* <!-- RENDER-THUMB:END --> ## See it next [![Probability|200](Probability_thumb.png)](Probability) *→ [[Probability|Probability]]* <!-- VISUAL-LINK:END --> --- Back to Signal Processing Portal · the room · Semiotic gateway <!-- REAL-GENERATIVE-MEDIA:START --> ## What it is A probability density function (PDF) is a non-negative function whose integral over an interval gives the probability that a continuous random variable falls within that interval; it integrates to one over its whole domain. ## How it works / why it matters PDFs describe how likely different amplitudes of a random signal or noise sample are — for example the Gaussian PDF for thermal noise or the uniform PDF for quantization error. In signal processing they are essential for statistical detection and estimation: likelihood functions, matched-filter derivations, and maximum-likelihood or Bayesian estimators are all built directly from the assumed density of the observations. ## Signs & universals Instantiates: - probability - noise - measurement ## Related [[Probability]] · Continuous variable · Thermal noise · Noise (physics) · [[Information_theory]] · Signal Processing <!-- VISUAL-LINK:START --> ## From the Real GENERATIVE library > In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variabl ([Wikipedia](https://en.wikipedia.org/wiki/Probability_density_function)) <!-- REAL-GENERATIVE-MEDIA:END --> <!-- CRAFT-LINK:START g12 --> *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].* <!-- CRAFT-LINK:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Probability_density_function) : [Wikitube](https://en.wikitube.io/wiki/Probability_density_function) ## Previous hub tags Tree parents: [[Dynamical_system]] · [[Monte_Carlo_method]] · [[Reliability_engineering]]. Legacy hubs: none. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*