Matching other characters to \left[ and \right]

Question

I have the following command for conditional expectations

\documentclass{article}
\newcommand{\E}[2]{E\left[ #1 \:|\: #2 \right]}

\begin{document}
\[ \E{\sum_{i=1}^N x_n}{Y} \]
\end{document}

The problem is that the | character looks ugly as it does not match the size of the surrounding square brackets. I would ideally put \big in front of it in this particular instance. I was wondering if there is a way to get the size of the text between \left and \right and use that to increase the size of | by some percentage.

Answer 1

Adapted from documentation of mathtools , § 3.6, Paired Delimiters, pp. 25–29. (Thanks to @Bernard).

\documentclass{article}
\usepackage{mathtools}

\makeatletter
\providecommand\given{}
\newcommand\@given[1][]{%
  \nonscript\:#1\vert \allowbreak \nonscript\:\mathopen{}}
\DeclarePairedDelimiterXPP\E[1]{E}[]{}{%
\renewcommand\given[1][\delimsize]{\@given[##1]}#1}
\makeatother

\begin{document}
\[ \E*{\sum_{i=1}^N x_n \given Y} \]
\end{document}

Answer 2

Here's another solution, also based on the mathtools package, but now making use of the \DeclarePairedDelimiterX macro as well as the \given and \Set macros set up on page 27 of the package's user guide.

The main user macro in the code below is called \expect. Observe that it inserts half of a thinspace to the right of the opening square bracket and to the left of the closing square bracket.

Incidentally, I think the E symbol ("expectation", right?) should be typeset as an upright-Roman character since it represents a math operator.

\documentclass{article}
\usepackage{mathtools}% for "\DeclarePairedDelimiterX" macro

% Expectation operator
\DeclareMathOperator{\E}{E} 

%% Three auxiliary macros: \given, \SetSymbol, and \Set
\providecommand\given{}
\newcommand\SetSymbol[1][]{% 
    \nonscript\:#1\vert\allowbreak\nonscript\:\mathopen{}}
\DeclarePairedDelimiterX\Set[1]\lbrack\rbrack{%
   \renewcommand\given{\SetSymbol[\delimsize]}#1}

%% Main user macro: \expect
\newcommand\expect[2][]{\E\Set[#1]{\mkern1.5mu#2\mkern1.5mu}}

\begin{document}

\[ 
\expect[\bigg]{\sum_{i=1}^N x_n\given Y} 
\qquad 
\expect[\Big]{\sum_{i=1}^N x_n}
\]

\end{document}

Answer 3

You can simply use the \middle primitive from e-TeX:

\def\E[#1|#2]{E\left[ #1 \>\middle|\> #2 \right]}

$$
  \E [\sum_{i=1}^N x_n | Y] 
$$

\bye

Note that more readable syntax is used.