Why is the expected value (mean) of a variable written using square brackets? My question is told in a few words: Why do you write $E[X]$ in square brackets instead of something like $E(X)$? Probably it is not a "function". How would you call it then? This question also applies for $Var[X]$.

I agree with all the above, but also it might has been inherited by the "brackets notation" used to notate discrete functions. For example, a discrete signal is notated as $x[n]$. Just saying...
