Approaching supervisor for master's thesis when I have ideas but nothing concrete? So I have to write my master's thesis, and I need to contact a potential supervisor. The field is statistics.

I am slightly confused by how these things work: on one hand, you often hear that you should have your own ideas and proposals for what you want to write about. On the other hand, your supervisor also needs to be able to supervise you, hence your ideas need to fall to his liking and be within his area of expertise and interest. 

With that in mind, how do I approach a potential supervisor? I intend to first write an e-mail. In this e-mail, do I 


merely introduce myself and my interests/coursework and then ask for the possibility of writing a master's thesis under their guidance, without getting into any specifics of what the topic should be, and then wait for their response? 
or do I specifically go into details with the ideas that I have in mind?
or do I mention my ideas vaguely but stress that I am open to any suggestions that he might have for a related topic?


I am learning towards option 3) as option 2) seems a bit too much for an initial contact and option 1) seems a bit lackluster.
Is this supervisor someone you know/in your department? This makes a  difference in your approach.
If this supervisor is from another school, and you REALLY want to work with them, go see who he has supervised in the past and reach out to them to get a feel for how that professor might respond. 


2a. An alternative to this is to call the departments graduate studies unit, convey your interest, and ask them how you might go about talking with a particular professor. Every university tends to have a prospective students section where you'll find an email for your questions to go to. 


If you are sending an email, prior to you getting into a bunch of details, it would probably save you some time to ask them if they are considering accepting graduate students for the 20xx-20yy year, and if they say yes, express your interest. 
Really make sure that you contact previous students to see how that professor is as a supervisor. This isn't done enough but it is so important to know what you're getting into.