Is it possible to install a full installation of Ubuntu on a USB stick?
As long as it’s over 2GB, yes. A 2GB stick is just a smidgen too small for a full install according to the Ubuntu installer (by literally a few MB). So if you grab a 4GB stick, yes, you can install a full version. Yes there are ways to get a full install of Ubuntu on a 2GB stick, however you’d have to do it not using the native Ubuntu installer. In other words, it’d be a pain at best to get it working. Besides which, running a full CD-sized distro on 2GB just isn’t smart because you’re guaranteed to run out of room fast. If you want a full install of Linux on 2GB-or-under sticks, consider Puppy Linux or Damn Small Linux, both of which can be pushed to USB stick with bootable ability via Unetbootin.