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:

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