I don't understand the difference in notation between E( expression ) and E[ expression ] for [expected value]. The Wikipedia article seems to indicate E( ) is used for an arbitrary function of X, but I'm not sure what the difference in meaning is.
Google pointed me to an example of a usage difference [here], but the article didn't help to resolve my misunderstanding much:
In the following the operations E[ ] and Var[ ] (square brackets as opposed to parentheses before !) mean expected value and variance with respect to the structure function (prior distribution) U(η, θ) over HxΘ.
Also, what does it mean when expected value is applied as an operator?.