Expected Values (Continuous Case)

expected value (continuous case)

The expected value or mean value of a continuous rv with PDF $f (x)$ is:

μ = μ_{X} = E (X) = \int_{- \infty}^{\infty} x \cdot f (x) d x

Proposition

If $X$ is a continuous rv with pdf $f (x)$ and $h (X)$ is any function of $X$ then:

μ_{h (X)} = E [h (X)] = \int_{- \infty}^{\infty} h (x) \cdot f (x) d t