# Why is it bad to multiply two expectations of the same variable?

In Sutton & Barto's book: Reinforcement Learning (chapter 11.5) they say that it is bad to multiply two expectations of the same variable, as otherwise the sample of the product will be biased.

Why is that the case?

Excerpt from the book: (part about bias missing)

This amounts to saying $E[x^2] \ne E[x] \cdot E[x]$. Now this is indeed the case in many situations. Consider that $x$ is normally distributed with mean $\mu$ and variance $\sigma^2$, then $E[x^2] = \mu^2 + \sigma^2 \ne E[x] \cdot E[x] = \mu^2$. So indeed, there is a constant bias by $\sigma^2$.