The Jew

Just so you know, the traditional answer (which Orthodox & Conservative Judaism adheres to) is that a Jew is someone whose mother was Jewish, or who converted into Judaism.

This means that Paris Hilton is Jewish as her grandmother is Liz Taylor.

Suppose I had a Jewish mother but was baptised as an infant. Would I still be Jewish?

Yes. If your mother was Jewish, you are Jewish for the rest of your life (according to traditional Judaism), no matter what you do. If you were brought up Christian and wanted to become Jewish, then you wouldn't need to convert if your mother were Jewish since you're already Jewish.