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Outcome Probabilities
Real Integrals
Needed by:
Cumulative Distribution Function From Density
Density Likelihood
Distribution Families
Maximum Likelihood Densities
Multivariate Real Densities
Normal Densities
Real Probability Densities
Uniform Densities
Sheet PDF
Graph PDF

Probability Densities


What if the set of outcomes is the real line, $\R $?


The principal difficulty is assigning nonzero numbers to infinitely many elements of a set. The solution is instead to assign probabilities to the events of outcomes, not to the individual outcomes (elementary events, real numbers), themselves.

A probability density (or probability density function (pdf)) is a function $f: \R \to \R $ satisfying $f \geq 0$ and $\int f = 1$.

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