Expected Value

• The “weighted average” of the values that a Random Variable can take on.

• It is usually denoted as:

  or or

Properties #

1. for any constant
   • So
2. for any constants

In the discrete case #

Assume is a discrete random variable and its corresponding Probability Mass Function .

In the continuous case #

Assume is a continuous random variable and its corresponding Probability Density Function .

What means #

discrete case

using a [Probability Mass Function](/uni/deep-learning/probability_mass_function/)

continous case

using a [Probability Density Function](/uni/deep-learning/probability_density_function/)