Editing Likelihood function (section)

==Products of likelihoods==
The likelihood, given two or more [[independence (probability theory)|independent]] [[Event (probability theory)|events]], is the product of the likelihoods of each of the individual events:
<math display="block">\Lambda(A \mid X_1 \land X_2) = \Lambda(A \mid X_1) \cdot \Lambda(A \mid X_2).</math>
This follows from the definition of independence in probability: the probabilities of two independent events happening, given a model, is the product of the probabilities.

This is particularly important when the events are from [[independent and identically distributed random variables]], such as independent observations or [[sampling with replacement]]. In such a situation, the likelihood function factors into a product of individual likelihood functions.

The empty product has value 1, which corresponds to the likelihood, given no event, being 1: before any data, the likelihood is always 1. This is similar to a [[uniform prior]] in Bayesian statistics, but in likelihoodist statistics this is not an [[improper prior]] because likelihoods are not integrated.