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:

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

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