Random letters and touch input on iPad
I've seen a couple variations of this problem before, and its usually one of 3 problems:


your touch screen is starting to malfunction. This is uncommon, but things happen with electronics. Seek repair from Apple.
Poorly conditioned electricity. Does this only happen when your iPad is plugged in? I had a generic plug that induced symptoms like you describe. Unplug the ipad and see if it still happens.
Liquid damage. This is probably the most frequent cause of electrical anomalies like this. Did anyone spill anything on the ipad, even if not recently?