Can I install Windows 7 on iPad 2?
It cannot be installed on the iPad 2. The processor in the iPad is an ARM processor and Windows (up to and including Windows 7) can only run on x86 processors, such as those from Intel and AMD. (There are other reasons that running Windows would be impossible, but this is the most important reason.)
Can I install Windows 7 on iPad 2?
No. Windows requires and runs on x86 architecture processors, while the iPad 2 has an ARM architecture processor.
Windows 8 does have an ARM option, and so does Android, so there is a small possibility in the distant future that someone will do the (significant!) work necessary to bring those systems to this hardware.
But windows 7 cannot be installed on the iPad 2, due primarily to the differences in CPU architecture.
I want to use Windows 7 on my iPad 2. Could it be done?
Yes, in a way. Typically what people do is they run windows on an network connected computer, then run a remote control app on the iPad. Windows 7 Professional comes with RDP, a remote desktop protocal which allows one to control the computer as if they were at the keyboard in front of the computer. They run an RDP client on the destination - in this case the iPad 2 - and can use the computer on the iPad 2.
This only works if you are on the same network, or if you're both connected to the internet and you have the network configuration set up correctly.
VNC is another popular protocol for which there are free servers and clients that would also allow you to use Windows 7 on your iPad 2 even though it's really running on another machine remotely.
If you ask a new question and give details as to how you want to use windows, how your network is currently set up, and details about the machine that's running windows, we can probably give you more detail as to the steps you would take to do this.
If you want to spend a little more money for a solution that just works without fiddling with configuring the computer, the iPad, or your network, then do a google search for "go to my pc" and you'll find several companies providing this service that take care of all the details for a low cost.
Other answers have addressed the problem with trying to run Windows 7 on an iPad, so instead, I will offer another workaround.
If you are looking for a way to run Windows 7 apps such as Microsoft Office on the iPad, one of the easiest non-VNC workarounds is to use OnLive. It connects over the Internet to one of OnLive's servers running Windows 7 and let's you use it as though it was installed on your iPad.
Here's a great article about OnLive from the New York Times: Windows on the iPad, and Speedy. They also mention how eventually it will let you run any application you want:
For example, the company intends to develop a third service, called OnLive Pro ($10 a month), that will let you run any Windows programs you want. Photoshop, Firefox, Autodesk, games — whatever.