Probabilities for a continuous random variable are described by areas under a probability density function (pdf), and this corresponds to an integral of the pdf. The rectangular distribution is introduced as a simple example.

The mean and variance of a continuous random variable, and the expected value of other functions can also be expressed as integrals.

Most commonly used continuous distributions also involve unknown parameters. The method of moments, maximum likelihood and confidence intervals can be used to estimate these parameter in a similar way to their use for discrete distributions.