Cool. To elaborate a bit more.. while "Big Data" is more than just Hadoop, I'd say that Hadoop is, for now, the Elephant In The Room (no pun intended), when it comes to Big Data processing. If we take that as a truism, I'd say:
If you want to get into the programming side of this stuff, you would be well served to spend some time learning Java. I know Java isn't considered the "coolest" language to know anymore, but if you want to work with Hadoop using the native APIs, well... it's written in Java. Now, that's not to say that you can't use Hadoop to distribute work in other languages (say, Python) but if you wanted to master Hadoop, some Java background would help, IMO.
Of course one nice thing about Hadoop isn't that you don't have to write directly to the map/reduce API in Java. There are layers built on top of it, that abstract some of that away... you get things like Pig, Cascading, etc. that make Hadoop easier to use. But knowing some Java will help if you want to hack on Hadoop itself, or if you need to write directly to the API for some reason.
If you have a good stats background but not much programming, I'd recommend start learning Java + Hadoop, and then grow outwards from there, pulling in other technologies (see above) as you go.