# Supplemental Proof: The Expected Value of a Squared Random Variable

We want to show the following relationship:

If we expand the first expression on the right-hand side of ** Equation 1**:

If we note that is a constant, then is also a constant, namely . Taking this into account ** Equation 2** simplifies to:

Plugging ** Equation 3** back into the right-hand side of

**gives**

*Equation 1*thus giving the desired result.