My new iPhone 5 keeps randomly beeping and vibrating?

I got a new iPhone 5 for Christmas and it was working perfectly fine for a few days. But then it started acting up. I usually have my phone in my back pocket and then one day it just randomly beeped and vibrated and I thought it was a text but it wasn't. It wasn't even a notification. So I have no idea what is going on or what is wrong with it.

You need to check your settings and see what makes it do that. It could be a email or some other program. I don know what programs you got on there.