Math mode expected value

You don't need to load bbold just for one of its symbols.

\documentclass{article}
\usepackage{amsmath,amssymb}

\DeclareRobustCommand{\bbone}{\text{\usefont{U}{bbold}{m}{n}1}}

\DeclareMathOperator{\EX}{\mathbb{E}}% expected value

\begin{document}

$\EX(f)+\bbone$

\end{document}

I found a solution. Instead of usepackage{bbold} which was necessary for {\mathbb{1}} otherwise they looked like this

I used the package bbm and \mathbbm{1}. With this both the expected value and 1 symbols look fine.