Custom alignment of text in itemized environment

What about this

\documentclass{article}
\begin{document}
$E[g(x)] = \int_{-\infty}^{+\infty} f_X(x) \, g(x) \, \mathrm{d}x$.
%
where,
%
\begin{itemize}
    \item{\makebox[2cm]{$x$\hfill} is a continuous random variable.}
    \item{\makebox[2cm]{$f_X(x)$\hfill} is the PDF of $x$.}
    \item{\makebox[2cm]{$g(x)$\hfill} is a function of $x$.}
\end{itemize}
\end{document} 

Output

You can avoid using \hfill for each item if you specify the second optional argument of \makebox to be the letter l (for left):

\documentclass{article}
\begin{document}
$E[g(x)] = \int_{-\infty}^{+\infty} f_X(x) \, g(x) \, \mathrm{d}x$.
%
where,
%
\begin{itemize}
    \item{\makebox[2cm][l]{$x$} is a continuous random variable.}
    \item{\makebox[2cm][l]{$f_X(x)$} is the PDF of $x$.}
    \item{\makebox[2cm][l]{$g(x)$} is a function of $x$.}
\end{itemize}
\end{document} 

I hope that itemize is only a suggestion. A simple solution without it.

\documentclass{article}
\begin{document}
$E[g(x)] = \int_{-\infty}^{+\infty} f_X(x) \, g(x) \, \mathrm{d}x$.
%
where

\begin{tabular}{@{$\bullet$ }ll}
   $x$      & is a continuous random variable.\\
   $f_X(x)$ & is the PDF of $x$.\\
   $g(x)$   & is a function of $x$.
\end{tabular}
\end{document}

Using a tabular as in @PrzemysławScherwentke's answer is a good way to go.

If you still wish to use itemize, here are two options, one without bullets and one with bullets.

\documentclass{article}

\begin{document}
$E[g(x)] = \int_{-\infty}^{+\infty} f_X(x) \, g(x) \, \mathrm{d}x$.
%
where,

% Without bullets
\begin{itemize}
    \item[$x$]{is a continuous random variable.}
    \item[$f_X(x)$]{is the PDF of $x$.}
    \item[$g(x)$]{is a function of $x$.}
\end{itemize}

% With bullets
\begin{itemize}
    \item{$x$\hphantom{$g(x)f_X(x)$} is a continuous random variable.}
    \item{$f_X(x)$\hphantom{$xg(x)$} is the PDF of $x$.}
    \item{$g(x)$\hphantom{$xf_X(x)$} is a function of $x$.}
\end{itemize}

\end{document}

The answer without bullets makes use of the optional argument of \item, which just gives the list item a label. The answer with bullets makes use of \hphantom{} to ensure that the amount of horizontal space taken up in each line is the same as in the other lines.