Problem: Variance and functions of random variable

Problem

• Suppose that $X$ is a discrete random variable. Show that $Var\left( X \right)=E\left( Y \right)$ where $Y={\left( X-μ_X \right)}^2$ and $μ_X=E(X)$ . We write $Var\left( X \right)=E{\left( X-μ_X \right)}^2$
• Same as a) but $X$ is a continuous random variable.