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.