Probability density function

A nonnegative function whose integral over a region gives the probability that a continuous random variable falls within that region. Its value at a point is not itself the probability of that exact outcome.

Probability measure: A mathematical assignment of probabilities to measurable events, obeying the axioms of probability. A density represents a probability measure through integration when such a density exists.
Random variable: A measurable function that assigns numerical values to outcomes of a random experiment. A density describes the distribution of a real-valued random variable.
Normal distribution: A continuous probability distribution with a symmetric, bell-shaped density determined by its mean and variance. Its familiar bell curve is a canonical probability density.
Likelihood function: A function of model parameters proportional to the probability or density of observed data. For continuous observations, likelihoods commonly use the model's density values.
Mixed distribution: A probability distribution with both discrete point masses and a continuous component. Its continuous component has a density, but the full distribution also assigns positive probability to points.
Cumulative distribution function: A function giving the probability that a random variable is less than or equal to each value. Integrating the density up to a value produces this function.
Continuous random variable: A real-valued random variable whose distribution assigns zero probability to every single point. Its interval probabilities can be represented by integrating a density.
Uniform distribution: A probability distribution assigning equal density throughout a bounded interval or region. Its constant density makes interval probabilities proportional to interval length.
Bayesian inference: A framework for updating probability distributions over hypotheses using observed evidence. Densities represent prior, likelihood, and posterior distributions for continuous parameters.
Singular distribution: A probability distribution concentrated on a set of zero length and lacking a density with respect to ordinary length. It shows that continuous-looking outcomes do not always admit an ordinary density.

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