If the desired length of a SOP is 1.5-2 pages, is it okay to have an extra page for bibliography? (so that I cite books/papers in the formal way)
Clarification: I mean 2 pages of text, plus 1 page of bibliography.
In my general experience, a statement of purpose rarely needs to be so detailed as to necessitate inclusion of a bibliography. That said, there is nothing expressly preventing you from including a bibliography. On the other hand, part of me is skeptical of the wisdom of including a full-page bibliography in association with a two-page statement. It may seem very much like overkill.
Unless you're citing each and every one of the works in the bibliography individually, I don't see a logical reason to include that many works. I'd stick to just the essential citations needed to explain what you want to do.