Expectation of a Utility Function

Question

I'm trying to understand how to calculate the expectation of a utility function, but not sure if I'm understanding it correctly... If your given a utility function $U(w)$ is $E[U(w)] = U(w)$?

Answer 1

In order to estimate the Expected Utility, you need a probability distribution over the set of possible $w$. Consider that $w$ is a random variable with p.d.f $f_W(w)$ and consider that $U(w)$ as the utility function (that depends on $w$).

To estimate the expected value apply the definition:

$$E(U(w))=\int U(w)f_W(w)dw$$

(if $w$ is discrete, then consider summing the values of $U(w)$ "weighted" by $P(W=w)$)