# The pdf and the cdf of a continuous random variable

Summary

- \(X\) is a continuous random variable with probability density function \(f\) and cumulative distribution function \(F\) . If \(F\) is differentiable then the relationship between the pdf and the cdf is as follows:

\[f\left( x \right)= \frac{dF\left( x \right)}{dx}\]

\[F\left( x \right)=\int_{-∞}^{x}{ f\left( u \right)du }\]