If a variable XXX has mean μ\muμ and variance σ2\sigma^2σ2, what is the variance of Y=X2Y = X^2Y=X2?
Var(X2)=E[X4]−μ4Var(X^2) = E[X^4] - \mu^4Var(X2)=E[X4]−μ4
Var(X2)=E[X4]−(E[X2])2Var(X^2) = E[X^4] - (E[X^2])^2Var(X2)=E[X4]−(E[X2])2
Var(X2)=4μ2σ2Var(X^2) = 4\mu^2\sigma^2Var(X2)=4μ2σ2
Var(X2)=σ4Var(X^2) = \sigma^4Var(X2)=σ4