Is statistics a pre-requisite to learn deep learning?
I would not call it a pre-requisite, but I would say reading books the that is necessary for knowing it all very well. 

I would recommend you to start with Andrew Ng's Machine Learning course on coursera.

Once you are familiar with that, move on to deep learning videos:


Nando de Freitas
Hugo Larochelle


While you are going through topics one after the other, go back to the books and read what they have to offer. Before you know, you would have done it all.

Good Luck!