Houjun Liu

continuous distribution

This is a continuous distribution for which the probability can be quantified as:

\begin{equation} p(x) \dd{x} \end{equation}

You will note that, at any given exact point, the probability is \(\lim_{\dd{x} \to 0} p(x)\dd{x} = 0\). However, to get the actual probability, we take an integral over some range:

\begin{equation} \int_{-\infty}^{\infty} p(x) \dd{x} = 1 \end{equation}

See also cumulative distribution function which represents the chance of something happening up to a threshold.