I have an question which links Taylor series to expectation and variance, but I'm really not sure what it's asking me to do.
X is exponential with rate 1.
The question asks me to use a three term Taylor series approximation for $\psi(X)=x^{-1\over 2}$ to approximate $\pi$ by evaluating $E[\psi(X)]$. And then use a two term Taylor's series approximation to approximate $Var(\psi(X))$. I'm really not certain how these steps link and how I would do the approximations.
Any help would be great. Thanks!