What is the expectation of a random variable raised to the $n$th power?

Question

If $Y=X^n$, with $n$ and the expectation and variance of $X$ known, what is the expectation and variance of $Y$?

Answer 1

Here's a partial answer: If $X$ is a Bernoulli variable, and $n\gt0$, then $E[X^n]=E[X]$ and $Var(X^n)=Var(X)$.