Empirical probability distribution
= Empirical probability distribution
{title2=$\widehat p(x)=n^{-1}\sum_{i=1}^n\mathbf1_{\{x_i=x\}}$}
For a nonempty finite sample, assign each distinct observed value its relative frequency. The observed values form the finite positive-mass support; the counts sum to the sample size, so the <probabilities> sum to one. Repeated observations increase the same outcome's mass rather than adding repeated support entries.