15.2 Discrete and Continuous

Some distributions apply to a discrete (i.e. countable) number of possibilities while others apply to continuous values. In the case of discrete variables, the probability is given by the actual value of the distribution, so it makes sense to speak of the probability of an individual label, $P({\rm coin 1})$. In the case of continuous variables, the probability is given by the area under the distribution, so it makes sense only to speak of the probability if a range of labels, $P(0.2 < \theta < 0.3)$.

Adapted from Statistical Inference for Everyone, by Brian Blais (Bryant University), licensed under CC BY-SA 4.0 (dual-licensed under the GNU FDL 1.2 or later; this adaptation uses the CC BY-SA grant). Changes were made; this adaptation is distributed under the same license. License: CC-BY-SA-4.0.