Definition and properties

• Definition: The expectation of a continuos random variable $X$ is $\mathbb{E}[X] = \displaystyle{ \int_{\Omega} } x \cdot f_X (x)\; dx$.

• The following properties still hold:

  • $\mathbb{E}[cX] = c\cdot \mathbb{E}[X]$
  • $\mathbb{E}[c + X] = c + \mathbb{E}[X]$