20
The Expected Value
In the last chapter, we learned about probability distributions, the objects that represent probabilistic models as sequences or functions. After all, there is the entire field of calculus to help us deal with functions, so they open up a wide array of mathematical tools.
However, we might not need all the information available. Sometimes, simple descriptive statistics such as mean, variance, or median suffice. Even in machine learning, loss functions are given in terms of them. For instance, the famous mean-squared error
is the variance of the prediction error. Deep down, these familiar quantities are rooted in probability theory, and we’ll devote this chapter to learning about them.
