Check again! The file is most likely in the folder C:\cygwin\usr\X11R6\bin (depending on where your cygwin base folder is located on your HD) on your lab system.
On your home PC you have either an incomplete CygWin installation, or an older version of CygWin installed.
In either case: Try reinstalling CygWin, use the internet-installation and make sure you have a recent version installed.
You can use "cygcheck -c" (located in the cygwin/bin folder) to check installed packages and compare their version to your lab PC's installation. "cygcheck -s" gives you a more detailed listing.