Given a transformation of the RV $X$, how do it's moments transform?
More Detailed Formulation
Suppose that $X:(\Omega,\mathcal{F},\mathbb{P})\rightarrow \mathbb{R}$, is a random variable whose MGF exists (ie: all its moments exist), and $f$ is a smooth function from $\mathbb{R}\rightarrow\mathbb{R}$. Denote by $\mu^{i}\triangleq \mathbb{E}^{\mathbb{P}}\left[(X)^i\right]$. Is there an expression for the $i^{th}$moment of $f(X)$ in terms of $\mu^1,\dots,\mu^i$?