I am currently starting my second year of PhD study in mathematics at an institution ranked 70-80 in math in the US. In my first year, I have taken some courses in probability theory and passed two of three qualifying exams.

After taking the probability courses and since my girlfriend is pursuing a master in statistics. I found myself really interested in statistics, is it wise to get another PhD in statistics after finishing PhD in math, or should I try to apply for a PhD in statistics now?

Is it possible for me to get admitted to an good institution(ranked 30-40 in US) with only some backgrounds in math?