Expected value of x to the power of a I would like to understand if $\mathbb{E}(x^a)$ is equal to $\mathbb{E}(x)^a$ if $0<a<1$. Generally I know that $\mathbb{E}(x^a) \neq \mathbb{E}(x)^a $ but under which conditions this could be not true?

It appears to be a homework assignment. So let me provide a hint.
Let $\phi(x) := x^a; ~a\in(0,1)$ be a real valued function.
Is it convex or concave? Compute $\phi^{\prime\prime}(x).$ Is it $>$ or $<0? $ For what values of $x? $ Then apply Jensen's Inequality. What does it yield?

NB. Please note whuber's comment.
