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A commutative diagram for en:conditional expectation. It isn't really commutative; instead it's commutative in an average sense. (Apparently that's what the dashed arrow indicates.)

David Benbennick made the diagram today, February 4, 2005. To make this image, I started with the following TeX file, diag.tex:

%&latex
\documentclass{article}
 \usepackage[matrix,arrow,ps]{xy}
 \UsePSspecials{dvips}
 \pagestyle{empty}

\begin{document}
 \[
 \xymatrix{
      & \mathbf{R} \\
 \Omega \ar@{->}[ur]^X \ar@{->}[r]_Y & U \ar@{-->}[u]_{\mathrm{E}(X\mid Y)}
 }
 \]
\end{document}

I ran the commands

tex diag
dvips -mode ljfzzz -D 1200 diag -o
convert -density 1200 -chop 4502x2515 -chop 99999x99999+1177+799 diag.ps diag.png
pngcrush -reduce -brute -l 9 diag.png diag.crush.png

The final output file was diag.crush.png.

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