centering a part of an equation

1. Aligned with \rightarrow

You can align it with the \rightarrow as such:

Notes:

• You can use align* so that you don't need to add \nonumber to each line.
• Usually you would not want to put the alignment at the beginning of the first term, so I have moved it to be before the \rightarrow.

---

2. Centered with \rightarrow:

A better solution is to use \makebox to get the vdots centered within the space of the \rightarrow:

Notes:

• This requires the use of the calc package.
• This has the benefit that no manual guessing of spacing is required. Hence, this solution can easily be adapted to other cases.

3. Centered with \rightarrow (with other enhancements)

I have provided another version which:

1. Incorporates Werner's recommendation of using Consistent typography by defining a \nat macro.

2. Incorporates egreg's recommendation to eliminate the space prior to the comma.

This yields:

---

Code: aligned with \rightarrow

\documentclass[12pt,letter]{report}


\usepackage{amsmath}

\begin{document}
\begin{align}
   X_{1} &\rightarrow\mathcal{N}\left(A\right) \nonumber \,,\\
  X_{2} &\rightarrow\mathcal{N}\left(B\right) \nonumber \,,\\
 &\vdots \nonumber
 \\X_{A-1} &\rightarrow\mathcal{N}\left(C\right) \nonumber\,, \\
X_{A} &\rightarrow\mathcal{N}\left(D\right) \nonumber \,, \\
  X &\rightarrow\mathcal{N}\left(E\right)\,.
  \end{align} 

\begin{align*}
   X_{1} &\rightarrow\mathcal{N}\left(A\right) \,,\\
  X_{2} &\rightarrow\mathcal{N}\left(B\right) \,,\\
 &\vdots \nonumber
 \\X_{A-1} &\rightarrow\mathcal{N}\left(C\right) \,, \\
X_{A} &\rightarrow\mathcal{N}\left(D\right) \,, \\
  X &\rightarrow\mathcal{N}\left(E\right)\,.
  \end{align*} 
\end{document} 

Code: centered with \rightarrow

\documentclass[12pt,letter]{report}


\usepackage{amsmath}
\usepackage{calc}

\begin{document}
\begin{align*}
   X_{1} &\rightarrow\mathcal{N}\left(A\right) \,,\\
  X_{2} &\rightarrow\mathcal{N}\left(B\right) \,,\\
 &\makebox[\widthof{${}\rightarrow{}$}][c]{\vdots}
 \\X_{A-1} &\rightarrow\mathcal{N}\left(C\right) \,, \\
X_{A} &\rightarrow\mathcal{N}\left(D\right) \,, \\
  X &\rightarrow\mathcal{N}\left(E\right)\,.
  \end{align*} 
\end{document} 

3. Code: centered with \rightarrow (with other enhancements)

\documentclass[12pt,letter]{report}

\usepackage{amsmath}
\usepackage{calc}

\newcommand{\nat}[1]{\mathcal{N}(#1)}

\begin{document}
\begin{align*}
     X_{1} &\rightarrow \nat{A}, \\
     X_{2} &\rightarrow \nat{B}, \\
           &\makebox[\widthof{${}\rightarrow{}$}][c]{\vdots} \\
   X_{A-1} &\rightarrow \nat{C}, \\
     X_{A} &\rightarrow \nat{D}, \\
         X &\rightarrow \nat{E}.
  \end{align*} 
\end{document} 

You can do it like this. Notice the additionally needed package mathtools:

\documentclass{article}

\usepackage{mathtools}

\begin{document}
\begin{align}
   X_{1} &\rightarrow\mathcal{N}\left(A\right) \nonumber \,,\\ 
   X_{2} &\rightarrow\mathcal{N}\left(B\right) \nonumber \,,\\ 
       &\,\mathclap{\phantom{\rightarrow}\vdots} \nonumber\\ 
   X_{A-1} &\rightarrow\mathcal{N}\left(C\right) \nonumber\,, \\ 
   X_{A} &\rightarrow\mathcal{N}\left(D\right) \nonumber \,, \\ 
   X &\rightarrow\mathcal{N}\left(E\right)\,.
\end{align} 

\end{document} 
\end{document} 

The construction \,\mathclap{\phantom{\rightarrow}\vdots} is a trick to make \vdots center with respect to the width of \rightarrow. As well, I consider the alignment by the arrows to be more proper here. (As @egreg correctly points out, I should have used a larger space \; here. However, this smaller one seems to work well because \rightarrow is an assymetric symbol.)

Yet another variation on the above:

\documentclass[12pt,letter]{report}
\usepackage{amssymb,amsmath}

\begin{document}
\begin{align}
    \begin{split}
X_{1}     & \rightarrow\mathcal{N}\left(A\right)  \,,\\ 
  X_{2}   & \rightarrow\mathcal{N}\left(B\right)  \,,\\ 
          &  \mspace{10mu}\vdots  \\ 
  X_{A-1} & \rightarrow\mathcal{N}\left(C\right) \,, \\ 
  X_{A}   & \rightarrow\mathcal{N}\left(D\right)  \,, \\ 
  X       & \rightarrow\mathcal{N}\left(E\right)\,.
    \end{split}
\end{align} 
\end{document}