Of interest to us is the cumulative probability distribution function (CDF), $P(x)$, which is just the probability for a stochastic variable $X$ to assume any value less than $x$ $$\begin{equation*} P(x)=\mathrm{Prob(}X\leq x\mathrm{)} = \int_{-\infty}^x p(x^{\prime})dx^{\prime}. \end{equation*}$$ The relation between a CDF and its corresponding PDF is then $$\begin{equation*} p(x) = \frac{d}{dx}P(x). \end{equation*}$$